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
In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic ...In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.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
A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expre...A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement.展开更多
A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The m...A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.展开更多
The concept of cointegration describes an equilibrium relationship among a set of time-varying variables, and the cointegrated relationship can be represented through an error-correction model (ECM). The error-correct...The concept of cointegration describes an equilibrium relationship among a set of time-varying variables, and the cointegrated relationship can be represented through an error-correction model (ECM). The error-correction variable, which represents the short-run discrepancy from the equilibrium state in a cointegrated system, plays an important role in the ECM. It is natural to ask how the error-correction mechanism works, or equivalently, how the short-run discrepancy affects the development of the cointegrated system? This paper examines the effect or local influence on the error-correction variable in an error-correction model. Following the argument of the second-order approach to local influence suggested by reference [5], we develop a diagnostic statistic to examine the local influence on the estimation of the parameter associated with the error-correction variable in an ECM. An empirical example is presented to illustrate the application of the proposed diagnostic. We find that the short-run discre pancy may have strong influence on the estimation of the parameter associated with the error-correction model. It is the error-correction variable that the short-run discrepancies can be incorporated through the error-correction mechanism.展开更多
Photodynamic therapy （PDT） has poor therapeutic outcomes for the treatment of port-wine stain （PWS） lesions with long drug-light intervals （DLIs）. This letter investigates the possibility of improving the treatm...Photodynamic therapy （PDT） has poor therapeutic outcomes for the treatment of port-wine stain （PWS） lesions with long drug-light intervals （DLIs）. This letter investigates the possibility of improving the treatment efficacy through increasing the laser power density using a computer simulation and a cock comb model. The computational model includes a Monte Carlo simulation for the laser distribution and a calculation of the singlet oxygen concentrations （102）. Both simulation and experimental results show that increasing the power density from i00 to 140 mW/cm^2 not only improves the PDT efficacy, but also results in the unwanted skin damage.展开更多
A new reasonably perfect dynamic mathematic model has been established for condenser used in ship nuclear power plant according to its structural features and operating principle. The model has been solved by the Rung...A new reasonably perfect dynamic mathematic model has been established for condenser used in ship nuclear power plant according to its structural features and operating principle. The model has been solved by the Runge-Kutta method. And an analysis program has been developed for dynamic numerical simulation under steady operation condition, disturbance condition, and accident condition. The dynamic characteristics of condenser has been calculated and analyzed under several kinds of disturbances, and the results of calculation are in good agreement with the theoretical analysis.展开更多
In order to establish the groove model for intersecting structures of circular tubes,mathematical model of the intersecting line is established by the method of analytic geometry,and parametric equations are thus dete...In order to establish the groove model for intersecting structures of circular tubes,mathematical model of the intersecting line is established by the method of analytic geometry,and parametric equations are thus determined.The dihedral angle,groove angle and actual cutting angle for any position of the intersecting line are derived as well.In order to identify groove vectors for two pipes,a new analytical method,i.e.coplanarity of vectors,is further proposed to complete the groove model.The established model is virtually verified by programming and simulation calculation in the MATLAB environment.The results show that groove vectors of intersecting structures simulated by MATLAB are consistent with the theoretical groove model,indicating that the theoretical groove model established in this paper is accurate,and further proves that the proposed coplanarity of vectors for solving groove vectors is correct and feasible.Finally,a graphical user interface(GUI)is developed by MATLAB software to independently realize functions such as model drawing,variable calculation and data output.The research outcome provides a theoretical foundation for the actual welding of circular intersecting structures,and lays an essential basis for weld bead layout and path planning.展开更多
This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the ...This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.展开更多
Analyses the cooling of mold and plastic part during injection molding and the continued cooling of plastic part after being ejected from mold using the heat transfer theory and Boundary Element Method (BEM) to predic...Analyses the cooling of mold and plastic part during injection molding and the continued cooling of plastic part after being ejected from mold using the heat transfer theory and Boundary Element Method (BEM) to predict the temperature distribution in both mold and plastic part,and presents the experiments carried out with plates of ABS (Acrylonitrile Butadiene Styrene) to verify the validity of the cooling analysis software used to simulate the temperature distribution in ABS plate parts, and concludes that the analysis software agree qualitatively well with actual experimental findings.展开更多
In this article,we introduce a nonlinear Caputo-type snakebite envenoming model with memory.The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractio...In this article,we introduce a nonlinear Caputo-type snakebite envenoming model with memory.The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractionalorder sense.The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector(L1-PC)scheme with error estimation and stability analysis.The proof of the existence and positivity of the solution is given by using the fixed point theory.From the necessary simulations,we justify that the first-time implementation of the proposedmethod on an epidemicmodel shows that the scheme is fully suitable and time-efficient for solving epidemic models.This work aims to show the novel application of the given scheme as well as to check how the proposed snakebite envenoming model behaves in the presence of the Caputo fractional derivative,including memory effects.展开更多
The current epidemic outbreak COVID-19 first took place in the Wuhan city of China and then spread worldwide.This deadly disease affected millions of people and compelled the governments and other concerned institutio...The current epidemic outbreak COVID-19 first took place in the Wuhan city of China and then spread worldwide.This deadly disease affected millions of people and compelled the governments and other concerned institutions to take serious actions.Around 0.28 million people have died from the COVID-19 outbreak as of May 11,2020,05:41 GMT,and the number is still increasing exponentially.The results of any scientific investigation of this phenomenon are still to come.However,now it is urgently needed to evaluate and compare the disease dynamics to improve the quarantine activities and the level of individual protection,to at least speed up the rate of isolation of infected persons.In the domain of big data science and other related areas,it is always of interest to provide the best description of the data under consideration.Therefore,in this article,we compare the COVID-19 pandemic dynamics between two neighboring Asian countries,Iran and Pakistan,to provide a framework to arrange the appropriate quarantine activities.Simple tools for comparing this deadly pandemic dynamic have been presented that can be adopted to produce the bases for inferences.Most importantly,a new statistical model is developed to provide the best description of COVID-19 daily deaths data in Iran and Pakistan.展开更多
A three-dimensional numerical model was developed to predict the behavior of tidal flow by using the σ-coordinate transformation. Conservation equations were solved by hybrid finite analytical techniques. The hydrody...A three-dimensional numerical model was developed to predict the behavior of tidal flow by using the σ-coordinate transformation. Conservation equations were solved by hybrid finite analytical techniques. The hydrodynamic model was verified with the analytical solutions for the tidal forcing in an open channel. The simulation results are in good agreement with the analytical solutions.展开更多
The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of su...The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of substrate and mediator are presented using He’s variational iteration method. The approximate expression of current for microheterogeneous catalysis at isonomer or redox polymer modified electrodes is also obtained. The results of the available limiting cases are compared with our results and are found to be in good agreement.展开更多
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The project was supported by the National Natural Science Faundation of China
文摘In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.
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.
文摘A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement.
文摘A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.
基金This project was supported by the National Natural Science Foundation (No. 79800012 and No. 79400014).
文摘The concept of cointegration describes an equilibrium relationship among a set of time-varying variables, and the cointegrated relationship can be represented through an error-correction model (ECM). The error-correction variable, which represents the short-run discrepancy from the equilibrium state in a cointegrated system, plays an important role in the ECM. It is natural to ask how the error-correction mechanism works, or equivalently, how the short-run discrepancy affects the development of the cointegrated system? This paper examines the effect or local influence on the error-correction variable in an error-correction model. Following the argument of the second-order approach to local influence suggested by reference [5], we develop a diagnostic statistic to examine the local influence on the estimation of the parameter associated with the error-correction variable in an ECM. An empirical example is presented to illustrate the application of the proposed diagnostic. We find that the short-run discre pancy may have strong influence on the estimation of the parameter associated with the error-correction model. It is the error-correction variable that the short-run discrepancies can be incorporated through the error-correction mechanism.
基金supported by the Key Program of National Natural Science Foundation of China(No.61036014)the National Natural Science Foundation of China(No.31170963)
文摘Photodynamic therapy （PDT） has poor therapeutic outcomes for the treatment of port-wine stain （PWS） lesions with long drug-light intervals （DLIs）. This letter investigates the possibility of improving the treatment efficacy through increasing the laser power density using a computer simulation and a cock comb model. The computational model includes a Monte Carlo simulation for the laser distribution and a calculation of the singlet oxygen concentrations （102）. Both simulation and experimental results show that increasing the power density from i00 to 140 mW/cm^2 not only improves the PDT efficacy, but also results in the unwanted skin damage.
文摘A new reasonably perfect dynamic mathematic model has been established for condenser used in ship nuclear power plant according to its structural features and operating principle. The model has been solved by the Runge-Kutta method. And an analysis program has been developed for dynamic numerical simulation under steady operation condition, disturbance condition, and accident condition. The dynamic characteristics of condenser has been calculated and analyzed under several kinds of disturbances, and the results of calculation are in good agreement with the theoretical analysis.
基金This work was supported by Natural Science Foundation of Fujian Province(Grant No.2020J01873)Science and Technology Major Project of Fujian Province(Grant No.2020HZ03018).
文摘In order to establish the groove model for intersecting structures of circular tubes,mathematical model of the intersecting line is established by the method of analytic geometry,and parametric equations are thus determined.The dihedral angle,groove angle and actual cutting angle for any position of the intersecting line are derived as well.In order to identify groove vectors for two pipes,a new analytical method,i.e.coplanarity of vectors,is further proposed to complete the groove model.The established model is virtually verified by programming and simulation calculation in the MATLAB environment.The results show that groove vectors of intersecting structures simulated by MATLAB are consistent with the theoretical groove model,indicating that the theoretical groove model established in this paper is accurate,and further proves that the proposed coplanarity of vectors for solving groove vectors is correct and feasible.Finally,a graphical user interface(GUI)is developed by MATLAB software to independently realize functions such as model drawing,variable calculation and data output.The research outcome provides a theoretical foundation for the actual welding of circular intersecting structures,and lays an essential basis for weld bead layout and path planning.
文摘This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.
文摘Analyses the cooling of mold and plastic part during injection molding and the continued cooling of plastic part after being ejected from mold using the heat transfer theory and Boundary Element Method (BEM) to predict the temperature distribution in both mold and plastic part,and presents the experiments carried out with plates of ABS (Acrylonitrile Butadiene Styrene) to verify the validity of the cooling analysis software used to simulate the temperature distribution in ABS plate parts, and concludes that the analysis software agree qualitatively well with actual experimental findings.
文摘In this article,we introduce a nonlinear Caputo-type snakebite envenoming model with memory.The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractionalorder sense.The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector(L1-PC)scheme with error estimation and stability analysis.The proof of the existence and positivity of the solution is given by using the fixed point theory.From the necessary simulations,we justify that the first-time implementation of the proposedmethod on an epidemicmodel shows that the scheme is fully suitable and time-efficient for solving epidemic models.This work aims to show the novel application of the given scheme as well as to check how the proposed snakebite envenoming model behaves in the presence of the Caputo fractional derivative,including memory effects.
基金supported by the Department of Statistics,Yazd University,Iran.
文摘The current epidemic outbreak COVID-19 first took place in the Wuhan city of China and then spread worldwide.This deadly disease affected millions of people and compelled the governments and other concerned institutions to take serious actions.Around 0.28 million people have died from the COVID-19 outbreak as of May 11,2020,05:41 GMT,and the number is still increasing exponentially.The results of any scientific investigation of this phenomenon are still to come.However,now it is urgently needed to evaluate and compare the disease dynamics to improve the quarantine activities and the level of individual protection,to at least speed up the rate of isolation of infected persons.In the domain of big data science and other related areas,it is always of interest to provide the best description of the data under consideration.Therefore,in this article,we compare the COVID-19 pandemic dynamics between two neighboring Asian countries,Iran and Pakistan,to provide a framework to arrange the appropriate quarantine activities.Simple tools for comparing this deadly pandemic dynamic have been presented that can be adopted to produce the bases for inferences.Most importantly,a new statistical model is developed to provide the best description of COVID-19 daily deaths data in Iran and Pakistan.
文摘A three-dimensional numerical model was developed to predict the behavior of tidal flow by using the σ-coordinate transformation. Conservation equations were solved by hybrid finite analytical techniques. The hydrodynamic model was verified with the analytical solutions for the tidal forcing in an open channel. The simulation results are in good agreement with the analytical solutions.
文摘The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of substrate and mediator are presented using He’s variational iteration method. The approximate expression of current for microheterogeneous catalysis at isonomer or redox polymer modified electrodes is also obtained. The results of the available limiting cases are compared with our results and are found to be in good agreement.
