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
In this paper, we used an efficient algorithm to obtain an analytic approximation for Volterra’s model for population growth of a species within a closed system, called the Restarted Adomian decomposition method (RAD...In this paper, we used an efficient algorithm to obtain an analytic approximation for Volterra’s model for population growth of a species within a closed system, called the Restarted Adomian decomposition method (RADM) to solve the model. The numerical results illustrate that RADM has the good accuracy.展开更多
The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are ...The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.展开更多
Kinetics of the decomposition of racemic ibuprofen crystals were studied by non-isothermal analysis. Thermogravimetric analysis revealed that ibuprofen is thermally stable up to 152.6°C and the initial loss of ma...Kinetics of the decomposition of racemic ibuprofen crystals were studied by non-isothermal analysis. Thermogravimetric analysis revealed that ibuprofen is thermally stable up to 152.6°C and the initial loss of mass was due to evaporation only. Activation energy, pre-exponential factor, activation entropy and Gibbs free energy for the decomposition of ibuprofen were determined using the integral method of Coats-Redfern (CR). Geometrical contraction models were found to be the best fits. The Arrheinus equation for the thermal decomposition of ibuprofen is k = (1.1 × 107) e–79125/RT sec–1.展开更多
The non-isothermal kinetics of CdO nanoparticles prepared from CdCO3 precursor using thermal decomposition method was investigated. A model-fitting Malek approach and a model-free advanced isoconversional method of Vy...The non-isothermal kinetics of CdO nanoparticles prepared from CdCO3 precursor using thermal decomposition method was investigated. A model-fitting Malek approach and a model-free advanced isoconversional method of Vyazovkin were applied to the analysis of the DSC and TGA data. The results showed that CdO nanoparticles prepared from CdCO3 followed an autocatalytic reaction. Sestak–Berggren model could favorably describe the studied reaction process. Moreover, the apparent activation energy of CdCO3 decomposition was calculated to be (119.19±9.97) kJ/mol and the explicit rate equation form of CdCO3 decomposition was established.展开更多
A mathematical model of an amperometric biosensor with the substrate inhibition for steady-state condition is discussed. The model is based on the system of non-stationary diffusion equation containing a non-linear te...A mathematical model of an amperometric biosensor with the substrate inhibition for steady-state condition is discussed. The model is based on the system of non-stationary diffusion equation containing a non-linear term related to non-Michaelis–Menten kinetics of the enzymatic reaction. This paper presents the analytical expression of concentrations and current for all values of parameters φ2s φ2s α and β . Here the Adomian decomposition method (ADM) is used to find the analytical expressions for substrate, product concentration and current. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.展开更多
In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and ...In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.展开更多
Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imag...Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imagery analyses only provide the displacement in the Line-of-Sight （LOS） direction or elevation changes. The 2004 Mid-Niigata earthquake in Japan provides lessons on how to decompose co-seismic deformation from two sets of DEMs. If three adjacent points undergo a rigid-body-translation movement, their co-seismic deformation can be decomposed by solving simultaneous equations. Although this method has been successfully used to discuss tectonic deformations, the algorithm needed improvement and a more rigorous algorithm, including a new definition of nominal plane, DEMs comparability improvement and matrix condition check is provided. Even with these procedures, the obtained decomposed displacement often showed remarkable scatter prompting the use of the moving average method, which was used to determine both tectonic and localized displacement characteristics. A cut-off window and a pair of band-pass windows were selected according to the regional geology and construction activities to ease the tectonic and localized displacement calculations, respectively. The displacement field of the tectonic scale shows two major clusters of large lateral components, and coincidently major visible landslides were found mostly within them. The localized displacement helps to reveal hidden landslides in the target area. As far as the Kizawa hamlet is concerned, the obtained vectors show down-slope movements, which are consistent with the observed traces of dislocations that were found in the Kizawa tunnel and irrigation wells. The method proposed has great potential to be applied to understanding post-earthquake rehabilitation in other areas.展开更多
The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the effi...The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.展开更多
Quantum mechanical and Rice-Ramsperger-Kassel-Marcus （RRKM） calculations are carried out to study the thermal unimolecular decomposition of 2,5-dihydrofuran （1）,2,5dihydrothiophene （2）,and 3-pyrroline （3） at t...Quantum mechanical and Rice-Ramsperger-Kassel-Marcus （RRKM） calculations are carried out to study the thermal unimolecular decomposition of 2,5-dihydrofuran （1）,2,5dihydrothiophene （2）,and 3-pyrroline （3） at the MPW1PW91/6-31＋＋G level of theory,and the results are in good agreement with the experimental values.The predicted high pressure limit rate constants （k（T）） in various states of activation energy and pre-exponential （S1：（A（calc.）,E a（calc.））,S2：（A （calc.）,E a（exp.））,and S3：（A （exp.）,E a（calc.））） for the thermal decomposition processes 1-3 were evaluated.Also,the fall-off pressures （P1/2） for compounds 1-3 in the states 1-3 are found to be （1.24×10-2,1.09×10-3,and 4.19×10-2mmHg）,（1.24×10-2,1.63×10-3,and 2.79×10-2mmHg）,and （1.24×10-2,1.63×10-3,and 4.19×10-2 mmHg）,respectively.As the fall-off pressure of thermal decomposition process of compounds 1-3 is in the following order：P1/2（3）〉 P1/2（1）〉 P1/2 （2）,the decomposition rates are as below：rate（3） 〈rate（1）〈rate（2）.展开更多
Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industr...Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.展开更多
In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional der...In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.展开更多
Digital twin is considered the key technique for real-time monitoring and life-cycle management of electric equipment.To construct the digital twin model of electric equipment,a multi-parameter electromagnetic analysi...Digital twin is considered the key technique for real-time monitoring and life-cycle management of electric equipment.To construct the digital twin model of electric equipment,a multi-parameter electromagnetic analysis is needed to generate a large amount of high fidelity data under various working condition.However,repeated solving such multi-parameter electromagnetic problems based on full order finite element method may lead to extreme scale calculations.To address this issue,a hybrid approach that combines tensor decomposition and proper orthogonal decomposition(POD)is introduced,which can effectively establish a reduced order model for multi-parameter electromagnetic field problems.The performance of the proposed approach is illustrated through three numerical examples,namely an electrical motor,a transformer and a voice coil actuator including parameter variations of operating conditions,geometric parameters,and material parameters.The numerical results show that the proposed hybrid approach has significant advantage compared to conventional reduced order model in situation where the solution changes dramatically within the parameter variation range and even more apparent when the parameter dimension is high.展开更多
Model validation and updating is critical to model credibility growth. In order to assess model credibility quantitatively and locate model error precisely, a new dynamic validation method based on extremum field mean...Model validation and updating is critical to model credibility growth. In order to assess model credibility quantitatively and locate model error precisely, a new dynamic validation method based on extremum field mean mode decomposition（EMMD） and the Prony method is proposed in this paper. Firstly, complex dynamic responses from models and real systems are processed into stationary components by EMMD. These components always have definite physical meanings which can be the evidence about rough model error location. Secondly, the Prony method is applied to identify the features of each EMMD component. Amplitude similarity, frequency similarity, damping similarity and phase similarity are defined to describe the similarity of dynamic responses.Then quantitative validation metrics are obtained based on the improved entropy weight and energy proportion. Precise model error location is realized based on the physical meanings of these features. The application of this method in aircraft controller design provides evidence about its feasibility and usability.展开更多
In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance m...In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.展开更多
Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations cont...Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations contains a non-linear term related to Monod kinetics, Andrews kinetics, interactive model from Monod kinetics and Andrews kinetics. Analytical expression of concentration of VOC (Volatile organic compounds) and oxygen are derived by solving the system of non-linear equations using Adomian decomposition method (ADM) method. Our analytical results are also compared with the simulation results. Satisfactory agreement is noted.展开更多
In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-...In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.展开更多
Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressibl...Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.展开更多
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In this paper, we used an efficient algorithm to obtain an analytic approximation for Volterra’s model for population growth of a species within a closed system, called the Restarted Adomian decomposition method (RADM) to solve the model. The numerical results illustrate that RADM has the good accuracy.
基金National Natural Science Foundation of China (No.10671153)
文摘The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.
文摘Kinetics of the decomposition of racemic ibuprofen crystals were studied by non-isothermal analysis. Thermogravimetric analysis revealed that ibuprofen is thermally stable up to 152.6°C and the initial loss of mass was due to evaporation only. Activation energy, pre-exponential factor, activation entropy and Gibbs free energy for the decomposition of ibuprofen were determined using the integral method of Coats-Redfern (CR). Geometrical contraction models were found to be the best fits. The Arrheinus equation for the thermal decomposition of ibuprofen is k = (1.1 × 107) e–79125/RT sec–1.
文摘The non-isothermal kinetics of CdO nanoparticles prepared from CdCO3 precursor using thermal decomposition method was investigated. A model-fitting Malek approach and a model-free advanced isoconversional method of Vyazovkin were applied to the analysis of the DSC and TGA data. The results showed that CdO nanoparticles prepared from CdCO3 followed an autocatalytic reaction. Sestak–Berggren model could favorably describe the studied reaction process. Moreover, the apparent activation energy of CdCO3 decomposition was calculated to be (119.19±9.97) kJ/mol and the explicit rate equation form of CdCO3 decomposition was established.
文摘A mathematical model of an amperometric biosensor with the substrate inhibition for steady-state condition is discussed. The model is based on the system of non-stationary diffusion equation containing a non-linear term related to non-Michaelis–Menten kinetics of the enzymatic reaction. This paper presents the analytical expression of concentrations and current for all values of parameters φ2s φ2s α and β . Here the Adomian decomposition method (ADM) is used to find the analytical expressions for substrate, product concentration and current. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.
文摘In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.
文摘Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imagery analyses only provide the displacement in the Line-of-Sight （LOS） direction or elevation changes. The 2004 Mid-Niigata earthquake in Japan provides lessons on how to decompose co-seismic deformation from two sets of DEMs. If three adjacent points undergo a rigid-body-translation movement, their co-seismic deformation can be decomposed by solving simultaneous equations. Although this method has been successfully used to discuss tectonic deformations, the algorithm needed improvement and a more rigorous algorithm, including a new definition of nominal plane, DEMs comparability improvement and matrix condition check is provided. Even with these procedures, the obtained decomposed displacement often showed remarkable scatter prompting the use of the moving average method, which was used to determine both tectonic and localized displacement characteristics. A cut-off window and a pair of band-pass windows were selected according to the regional geology and construction activities to ease the tectonic and localized displacement calculations, respectively. The displacement field of the tectonic scale shows two major clusters of large lateral components, and coincidently major visible landslides were found mostly within them. The localized displacement helps to reveal hidden landslides in the target area. As far as the Kizawa hamlet is concerned, the obtained vectors show down-slope movements, which are consistent with the observed traces of dislocations that were found in the Kizawa tunnel and irrigation wells. The method proposed has great potential to be applied to understanding post-earthquake rehabilitation in other areas.
基金supported by the Innovation Fund Project of the Gansu Education Department(Grant No.2021B-099).
文摘The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.
文摘Quantum mechanical and Rice-Ramsperger-Kassel-Marcus （RRKM） calculations are carried out to study the thermal unimolecular decomposition of 2,5-dihydrofuran （1）,2,5dihydrothiophene （2）,and 3-pyrroline （3） at the MPW1PW91/6-31＋＋G level of theory,and the results are in good agreement with the experimental values.The predicted high pressure limit rate constants （k（T）） in various states of activation energy and pre-exponential （S1：（A（calc.）,E a（calc.））,S2：（A （calc.）,E a（exp.））,and S3：（A （exp.）,E a（calc.））） for the thermal decomposition processes 1-3 were evaluated.Also,the fall-off pressures （P1/2） for compounds 1-3 in the states 1-3 are found to be （1.24×10-2,1.09×10-3,and 4.19×10-2mmHg）,（1.24×10-2,1.63×10-3,and 2.79×10-2mmHg）,and （1.24×10-2,1.63×10-3,and 4.19×10-2 mmHg）,respectively.As the fall-off pressure of thermal decomposition process of compounds 1-3 is in the following order：P1/2（3）〉 P1/2（1）〉 P1/2 （2）,the decomposition rates are as below：rate（3） 〈rate（1）〈rate（2）.
文摘Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.
文摘In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.
基金supported by the UCAS-ULille joint PhD training program and also partially supported within the frame of the EE4.0(Electrical Energy 4.0)project,which is co-financed by the European Union,with the financial support of the European Regional Development Fund(ERDF),the French state,and the French Region of Hautsde-France.
文摘Digital twin is considered the key technique for real-time monitoring and life-cycle management of electric equipment.To construct the digital twin model of electric equipment,a multi-parameter electromagnetic analysis is needed to generate a large amount of high fidelity data under various working condition.However,repeated solving such multi-parameter electromagnetic problems based on full order finite element method may lead to extreme scale calculations.To address this issue,a hybrid approach that combines tensor decomposition and proper orthogonal decomposition(POD)is introduced,which can effectively establish a reduced order model for multi-parameter electromagnetic field problems.The performance of the proposed approach is illustrated through three numerical examples,namely an electrical motor,a transformer and a voice coil actuator including parameter variations of operating conditions,geometric parameters,and material parameters.The numerical results show that the proposed hybrid approach has significant advantage compared to conventional reduced order model in situation where the solution changes dramatically within the parameter variation range and even more apparent when the parameter dimension is high.
基金supported by the Nature Science Foundation of Shaanxi Province(2012JM8020)
文摘Model validation and updating is critical to model credibility growth. In order to assess model credibility quantitatively and locate model error precisely, a new dynamic validation method based on extremum field mean mode decomposition（EMMD） and the Prony method is proposed in this paper. Firstly, complex dynamic responses from models and real systems are processed into stationary components by EMMD. These components always have definite physical meanings which can be the evidence about rough model error location. Secondly, the Prony method is applied to identify the features of each EMMD component. Amplitude similarity, frequency similarity, damping similarity and phase similarity are defined to describe the similarity of dynamic responses.Then quantitative validation metrics are obtained based on the improved entropy weight and energy proportion. Precise model error location is realized based on the physical meanings of these features. The application of this method in aircraft controller design provides evidence about its feasibility and usability.
文摘In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.
文摘Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations contains a non-linear term related to Monod kinetics, Andrews kinetics, interactive model from Monod kinetics and Andrews kinetics. Analytical expression of concentration of VOC (Volatile organic compounds) and oxygen are derived by solving the system of non-linear equations using Adomian decomposition method (ADM) method. Our analytical results are also compared with the simulation results. Satisfactory agreement is noted.
文摘In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.
文摘Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.
