Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory ca...Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.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
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
Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing. Based on gas trapping theory and the mass conservation equation, mathemati...Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing. Based on gas trapping theory and the mass conservation equation, mathematical models were developed for foam-diverted acidizing, which can be achieved by a foam slug followed by acid injection or by continuous injection of foamed acid. The design method for foam-diverted acidizing was also given. The mathematical models were solved by a computer program. Computed results show that the total formation skin factor, wellhead pressure and bottomhole pressure increase with foam injection, but decrease with acid injection. Volume flow rate in a highpermeability layer decreases, while that in a low-permeability layer increases, thus diverting acid to the low-permeability layer from the high-permeability layer. Under the same formation conditions, for foamed acid treatment the operation was longer, and wellhead and bottomhole pressures are higher. Field application shows that foam slug can effectively block high permeability layers, and improve intake profile noticeably.展开更多
A mathematical model to describe the seam-cavity growth during underground coal gasification(UCG) is developed. The effect of coal gasification or coal combustion on lateral growth of coal wall is mainly considered in...A mathematical model to describe the seam-cavity growth during underground coal gasification(UCG) is developed. The effect of coal gasification or coal combustion on lateral growth of coal wall is mainly considered in this model. It is based on some basic assumptions and balances of heat and mass transfer in gasification zone of cavity,and considers the effect of dry distillation of seams. The gasifing zone of coal wall is assumpted to be a thin,highly permeable char layer and an ash layer seperating inert ash rubble of the main cavity from coal wall. The model can explain lateral growth mechanism of coal wall in entire gasification process,and determine the growth velocity v (x,t) of coal wall.展开更多
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...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.展开更多
The regular pattern of temperature change in a coalfield fire area while the fire is being extinguished was studied. To determine the extinguishing effect, a series of linear, logarithmic, polynomial or exponential ma...The regular pattern of temperature change in a coalfield fire area while the fire is being extinguished was studied. To determine the extinguishing effect, a series of linear, logarithmic, polynomial or exponential mathematical regression models were constructed using the observed temperature data from the Xinjiang coalfield fire extinguishing project. The quadratic polynomial mathematical model had the best fit. A large coal fire oven was also used to simulate the coal fire extinguishing process. The same mathematical regression experiments were carried out on that observed data. The results verified that the quadratic polynomial mathematical model had the best fit. Therefore, a quadratic polynomial mathematical model is proposed to accurately model the temperature-time relationship in a coalfield fire area. An application to coalfield fire suppression shows that the deduced mathe-matical model can be used to predict the temperature conditions and to determine the effect of fire extinguishing, thereby helping to speed up the fire suppression process in the coalfield fire area.展开更多
In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of memb...In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of membrane module is very useful in achieving guidelines for design and characterization of membrane separation units. In this study, a model based on Coker, Freeman, and Fleming＇s study was used for estimating the required membrane area. This model could simulate a multicomponent gas mixture separation by solving the governing differential mass balance equations with numerical methods. Results of the model were validated using some binary and multicomponent experimental data from the literature. Also, the artificial neural network （ANN） technique was applied to predict membrane gas separation behavior and the results of the ANN simulation were compared with the simulation results of the model and the experimental data. Good consistency between these results shows that ANN method can be successfully used for prediction of the separation behavior after suitable training of the network展开更多
By the sketch of structure of MVWG,the working laws of this kind of gyroscope we re explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic workin...By the sketch of structure of MVWG,the working laws of this kind of gyroscope we re explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.展开更多
Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas le...Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas leakage prevention.This study presents a numerical investigation of foam behavior in a porous medium.Fractional flow method is applied to describe steady-state foam displacement in the entrance region.In this model,foam flow for the cases of excluding and including capillary pressure and for two types of gas,nitrogen(N2)and carbon dioxide(CO2)are investigated.Effects of pertinent parameters are also verified.Results indicate that the foam texture strongly governs foam flow in porous media.Required entrance region may be quite different for foam texture to accede local equilibrium,depending on the case and physical properties that are used.According to the fact that the aim of foaming of injected gas is to reduce gas mobility,results show that CO2 is a more proper injecting gas than N2.There are also some ideas presented here on improvement in foam displacement process.This study will provide an insight into future laboratory research and development of full-field foam flow in a porous medium.展开更多
The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined q...The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined quantitatively by mathematical model. The tight gas charging and accumulation mechanisms were revealed from a combination of physical simulation of nuclear magnetic resonance coupling displacement, numerical simulation considering material and mechanical equilibria, as well as actual geological observation. The results show that gas migrates into tight rocks to preferentially form a gas saturation stabilization zone near the source-reservoir interface. When the gas source is insufficient, gas saturation reduction zone and uncharged zone are formed in sequence from the source-reservoir interface. The better the source rock conditions with more gas expulsion volume and higher overpressure, the thicker the gas saturation stabilization and reduction zones, and the higher the overall gas saturation. When the source rock conditions are limited, the better the tight reservoir conditions with higher porosity and permeability as well as larger pore throat, the thinner the gas saturation stabilization and reduction zones, but the gas saturation is high. The sweet spot of tight gas is developed in the high-quality reservoir near the source rock, which often corresponds to the gas saturation stabilization zone. The numerical simulation results by mathematical model agree well with the physical simulation results by nuclear magnetic resonance coupling displacement, and reasonably explain the gas-water distribution and production pattern of deep reservoirs in the Xujiaweizi fault depression of the Songliao Basin and tight gas reservoirs in the Linxing-Huangfu area of the Ordos Basin.展开更多
To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are show...To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.展开更多
Through analyzing the movement characteristics of particles and particle group in jig bed, the mathematical model of jig stratifying process is established with Markov chain theory and it has been examined by stratify...Through analyzing the movement characteristics of particles and particle group in jig bed, the mathematical model of jig stratifying process is established with Markov chain theory and it has been examined by stratifying test with laboratory U-type jig. The experiment shows that the mathematical model can describe jig stratifying process well.展开更多
A mathematical model of the bellows dispersion system is developed by combining the interior ballistic theory with structural dynamics theory to describe the deformation course of bellows. By analyzing the physical mo...A mathematical model of the bellows dispersion system is developed by combining the interior ballistic theory with structural dynamics theory to describe the deformation course of bellows. By analyzing the physical model of the bellows dispersion system, the dispersion course is divided into three stages. For each stage, mathematical model is built and its terminal conditions are given. The numerical simulation is based on the Runge-Kutta method and differential quadrature method. Simulation results of the model agree with those of the model built by only interior ballistics theory. However, this model is congruous with the actual dispersion course and can more easily determine the dispersion time and submunition displacement.展开更多
The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of t...The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.展开更多
Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied T...Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.展开更多
Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the grou...Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method （IBEM） and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground （WIG） effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a 4° Angle of Attack （AoA） which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft.展开更多
基金supported by the National Natural Science Foundation of China(11871238,11931019,12371486)。
文摘Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.
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.
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.
文摘Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing. Based on gas trapping theory and the mass conservation equation, mathematical models were developed for foam-diverted acidizing, which can be achieved by a foam slug followed by acid injection or by continuous injection of foamed acid. The design method for foam-diverted acidizing was also given. The mathematical models were solved by a computer program. Computed results show that the total formation skin factor, wellhead pressure and bottomhole pressure increase with foam injection, but decrease with acid injection. Volume flow rate in a highpermeability layer decreases, while that in a low-permeability layer increases, thus diverting acid to the low-permeability layer from the high-permeability layer. Under the same formation conditions, for foamed acid treatment the operation was longer, and wellhead and bottomhole pressures are higher. Field application shows that foam slug can effectively block high permeability layers, and improve intake profile noticeably.
文摘A mathematical model to describe the seam-cavity growth during underground coal gasification(UCG) is developed. The effect of coal gasification or coal combustion on lateral growth of coal wall is mainly considered in this model. It is based on some basic assumptions and balances of heat and mass transfer in gasification zone of cavity,and considers the effect of dry distillation of seams. The gasifing zone of coal wall is assumpted to be a thin,highly permeable char layer and an ash layer seperating inert ash rubble of the main cavity from coal wall. The model can explain lateral growth mechanism of coal wall in entire gasification process,and determine the growth velocity v (x,t) of coal wall.
基金The financial supports received from the National Natural Science Foundation of China(21522609,21636009 and 21878328)the National Key Research and Development Program of China(Nos.2017YFC0307302,2016YFC0304003)+1 种基金the Science Foundation of China University of Petroleum,Beijing(No.2462018BJC004)Beijing Science and Technology Program,China(No.Z181100005118010)。
文摘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.
基金Project 50474031 supported by the National Natural Science Foundation of China
文摘The regular pattern of temperature change in a coalfield fire area while the fire is being extinguished was studied. To determine the extinguishing effect, a series of linear, logarithmic, polynomial or exponential mathematical regression models were constructed using the observed temperature data from the Xinjiang coalfield fire extinguishing project. The quadratic polynomial mathematical model had the best fit. A large coal fire oven was also used to simulate the coal fire extinguishing process. The same mathematical regression experiments were carried out on that observed data. The results verified that the quadratic polynomial mathematical model had the best fit. Therefore, a quadratic polynomial mathematical model is proposed to accurately model the temperature-time relationship in a coalfield fire area. An application to coalfield fire suppression shows that the deduced mathe-matical model can be used to predict the temperature conditions and to determine the effect of fire extinguishing, thereby helping to speed up the fire suppression process in the coalfield fire area.
文摘In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of membrane module is very useful in achieving guidelines for design and characterization of membrane separation units. In this study, a model based on Coker, Freeman, and Fleming＇s study was used for estimating the required membrane area. This model could simulate a multicomponent gas mixture separation by solving the governing differential mass balance equations with numerical methods. Results of the model were validated using some binary and multicomponent experimental data from the literature. Also, the artificial neural network （ANN） technique was applied to predict membrane gas separation behavior and the results of the ANN simulation were compared with the simulation results of the model and the experimental data. Good consistency between these results shows that ANN method can be successfully used for prediction of the separation behavior after suitable training of the network
文摘By the sketch of structure of MVWG,the working laws of this kind of gyroscope we re explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.
文摘Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas leakage prevention.This study presents a numerical investigation of foam behavior in a porous medium.Fractional flow method is applied to describe steady-state foam displacement in the entrance region.In this model,foam flow for the cases of excluding and including capillary pressure and for two types of gas,nitrogen(N2)and carbon dioxide(CO2)are investigated.Effects of pertinent parameters are also verified.Results indicate that the foam texture strongly governs foam flow in porous media.Required entrance region may be quite different for foam texture to accede local equilibrium,depending on the case and physical properties that are used.According to the fact that the aim of foaming of injected gas is to reduce gas mobility,results show that CO2 is a more proper injecting gas than N2.There are also some ideas presented here on improvement in foam displacement process.This study will provide an insight into future laboratory research and development of full-field foam flow in a porous medium.
基金Supported by the National Natural Science Foundation of China(42302183,42272156,41922015)Sanya City Science and Technology Innovation Project(2022KJCX51).
文摘The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined quantitatively by mathematical model. The tight gas charging and accumulation mechanisms were revealed from a combination of physical simulation of nuclear magnetic resonance coupling displacement, numerical simulation considering material and mechanical equilibria, as well as actual geological observation. The results show that gas migrates into tight rocks to preferentially form a gas saturation stabilization zone near the source-reservoir interface. When the gas source is insufficient, gas saturation reduction zone and uncharged zone are formed in sequence from the source-reservoir interface. The better the source rock conditions with more gas expulsion volume and higher overpressure, the thicker the gas saturation stabilization and reduction zones, and the higher the overall gas saturation. When the source rock conditions are limited, the better the tight reservoir conditions with higher porosity and permeability as well as larger pore throat, the thinner the gas saturation stabilization and reduction zones, but the gas saturation is high. The sweet spot of tight gas is developed in the high-quality reservoir near the source rock, which often corresponds to the gas saturation stabilization zone. The numerical simulation results by mathematical model agree well with the physical simulation results by nuclear magnetic resonance coupling displacement, and reasonably explain the gas-water distribution and production pattern of deep reservoirs in the Xujiaweizi fault depression of the Songliao Basin and tight gas reservoirs in the Linxing-Huangfu area of the Ordos Basin.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11572025,11202013 and 51420105008
文摘To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.
文摘Through analyzing the movement characteristics of particles and particle group in jig bed, the mathematical model of jig stratifying process is established with Markov chain theory and it has been examined by stratifying test with laboratory U-type jig. The experiment shows that the mathematical model can describe jig stratifying process well.
文摘A mathematical model of the bellows dispersion system is developed by combining the interior ballistic theory with structural dynamics theory to describe the deformation course of bellows. By analyzing the physical model of the bellows dispersion system, the dispersion course is divided into three stages. For each stage, mathematical model is built and its terminal conditions are given. The numerical simulation is based on the Runge-Kutta method and differential quadrature method. Simulation results of the model agree with those of the model built by only interior ballistics theory. However, this model is congruous with the actual dispersion course and can more easily determine the dispersion time and submunition displacement.
文摘The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.
基金supported by the National Natural Science Foundation of China (No. 51475233)the Natural Science Foundation of Jiangsu Province(No. BK20171170)+2 种基金the Six Talent Peaks Project of Jiangsu Province(No. JXQC-049)the Major Program of the Natural Science Foundation for Colleges and Universities of Jiangsu Province(No. 19KJA560007)the Project of Jiangsu Key Laboratory of Large Engineering Equipment Detection and Control(No. JSKLEDC201512)
文摘Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.
基金Supported by Yildiz Technical University Scientific Research Projects Coordination Department under Project No.2013-10-01-KAP02
文摘Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method （IBEM） and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground （WIG） effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a 4° Angle of Attack （AoA） which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft.
