This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence ...This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.展开更多
In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to ana...In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.展开更多
A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equati...A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.展开更多
1 Development of UHVDC transmission capabilities The economical development of China is closely connected with safe and reliable power supply.Load centers e.g.in central and eastern China need huge amounts of electric...1 Development of UHVDC transmission capabilities The economical development of China is closely connected with safe and reliable power supply.Load centers e.g.in central and eastern China need huge amounts of electrical power.Available energy resources and consumption areas are often distributed inverse.As a consequence it is necessary to import electrical power to load center areas in an economic and efficient way.展开更多
In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material a...In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material and heat source spatial distributions are then derived with the help of transformation method. The construction of mapping by grid generation method through solving partial differential equations circumvents the limitation of device geometry, which paves the way for designing more complex heat flow control devices. Two numerical examples are also given to show how to design material properties and heat source in order to control temperature patterns.展开更多
In this paper,we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method,many explicit and exact general solutions with arbitrary funct...In this paper,we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method,many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations,which contain solitary wave solutions,trigonometric function solutions,and rational solutions,are obtained.展开更多
In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the...In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the fin heat dissipating capacity but the internal heat generation decreases the heat enhancement capacity of extended surface.Also,it is established that when the internal heat parameter increases to some certain values,some negative effects are recorded where the fin stores heat rather than dissipating it.This scenario defeats the prime purpose of the cooling fin.Additionally,it is established in the present study that the limiting value of porosity parameter for thermal stability for the passive device increases as internal heat parameter increases.This shows that although the internal heat parameter can help assist higher range and value of thermal stability of the fin,it produces negative effect which greatly defeats the ultimate purpose of the fin.The results in the work will help in fin design for industrial applications where internal heat generation is involved.展开更多
In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This s...In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This semi-analytic method has the advantage of overcoming the obstacle of the hardest nonlinear terms and is used to explain the origin of the bright and dark soliton solutions through the Schrödinger equation in its non-local form and the Radhakrishnan-Kundu-Laksmannan (RKL) equation. Numerical examples demonstrate the effectiveness of this method.展开更多
The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results sh...The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.展开更多
Through active manipulation of wavelengths,a structure exposed to a water-wave field can achieve a target hydrodynamic performance.Based on the form invariance of the governing equation for shallow water waves,wavelen...Through active manipulation of wavelengths,a structure exposed to a water-wave field can achieve a target hydrodynamic performance.Based on the form invariance of the governing equation for shallow water waves,wavelength modulators have been proposed using the space transformation method,which enables wavelength manipulation by distributing an anisotropic medium that incorporates water depth and gravitational acceleration within the modulation space.First,annular wavelength modulators were designed using the space transformation method to reduce or amplify the wavelength of shallow water waves.The control method of wavelength scaling ratios was investigated.In addition to plane waves,the wavelength modulator was applied to manipulate the wavelength of cylindrical waves.Furthermore,the interactions between a vertical cylinder and modulated water waves were studied.Results indicate that the wavelength can be arbitrarily reduced or amplified by adjusting the dimensional parameters of the modulator.Additionally,the modulator is effective for plane waves and cylindrical waves.This wavelength modulator can enable the structure to achieve the desired scattering characteristics at the target wavelength.展开更多
Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a num...Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a number of track parameters.One possible reason for deviations between simulated and measured results for the dynamic track behaviour is the uncertainty of the value of some track parameters used as input for the simulation.This in turn results in an uncertainty in the simulation results.In this contribution,it is proposed to use the general transformation method to assess a uncertainty band for the results.Most relevant input parameters for determining the point input mobility and the track decay rate for a ballasted track are analysed with regard to the uncertainties and for the value of each an interval is determined.Then,the general transformation method is applied to four different simulation methods,working both in the frequency and time domains.For one example track,the resulting uncertainty bands are compared to one dataset with measurements for the point mobility and the track decay rate.In addition,a sensitivity analysis is performed to determine the parameters that significantly influence the overall result.While all four simulation methods produce broad uncertainty bands for the results,none did match the measured results for the point mobility and the track decay rate over the entire frequency range considered.Besides the large influence of the uncertain pad stiffness,it turned out that the rail wear is also a significant source of uncertainty of the results.Overall,it is demonstrated that the proposed approach allows assessing the influence of uncertain input parameters in detail.展开更多
At present, transgenic technologies have become important means of plant breeding, and the application and promotion of transgenic technologies have created huge economic and social benefits. Transgenic plant products...At present, transgenic technologies have become important means of plant breeding, and the application and promotion of transgenic technologies have created huge economic and social benefits. Transgenic plant products have significantly affected human life. Anthurium andraeanum is the second major tropical potted flower and its transgenic breeding has a promising prospect of application. In this paper, acceptors, transformation methods and introduced exogenous genes （ including reporter genes, selectable marker genes and target genes） of Anthurium andraeanum were summarized; in addition, several issues related to transforma- tion of Anthurium andraeanum were analyzed, aiming at providing reference for transgenic breeding of Anthurium andraeanum.展开更多
Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy,low friction,low noise and high stability.The rotor system with axial-grooved gas-lubricated jo...Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy,low friction,low noise and high stability.The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system.The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail.The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory.A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing.The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method.The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system,and the dynamic equation of motion is calculated by the modified Wilson-0-based method.To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings,such as bifurcation and chaos,the bifurcation diagram,the orbit diagram,the Poincar6 map,the time series and the frequency spectrum are employed.The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena,such as the periodic,period-doubling,quasi-periodic,period-4 and chaotic motion,and so on.The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.展开更多
Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytical...Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytically using differential transformation method. Velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are determined analytically. The influence of pertinent parameters such as magnetic parameter, nanofluid volume fraction, viscosity parameter and Eckert number on the flow and heat transfer characteristics is discussed. Results indicate that skin friction coefficient decreases with increase of magnetic parameter, nanofluid volume fraction and viscosity parameter. Nusselt number increases with increase of magnetic parameter and nanofluid volume fraction while it decreases with increase of Eckert number and viscosity parameter.展开更多
The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more...The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more practical results, this study considers a cubic polynomial relationship between the humidity ratio of saturated air and the corresponding fin surface temperature. The temperature distribution has been determined by solving the highly non-linear governing equations using a semi-analytical transformation technique called Differential Transform Method. A comparison of the results with that of a numerical model shows that this transformation method is a very efficient and convenient tool for solution of non-linear problems. The effects of various geometric, thermo-physical and psychometric parameters on the temperature distribution, fin efficiency and optimum design condition have been investigated. Also, a comparison has been presented between solid and porous fins and the results point out that by selecting an appropriate value of porosity, the heat transfer rate can be increased than the corresponding solid fin.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t...We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.展开更多
The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious...The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.展开更多
This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculat...This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.展开更多
文摘This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.
基金The project partly supported by the Foundation of Zhongshan University Advanced Research Center
文摘In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.
文摘1 Development of UHVDC transmission capabilities The economical development of China is closely connected with safe and reliable power supply.Load centers e.g.in central and eastern China need huge amounts of electrical power.Available energy resources and consumption areas are often distributed inverse.As a consequence it is necessary to import electrical power to load center areas in an economic and efficient way.
基金supported by the National Natural Science Foundation of China(Nos.11372035,10832002 and 11221202)China Postdoctoral Science Foundation(No.2014M550054)
文摘In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material and heat source spatial distributions are then derived with the help of transformation method. The construction of mapping by grid generation method through solving partial differential equations circumvents the limitation of device geometry, which paves the way for designing more complex heat flow control devices. Two numerical examples are also given to show how to design material properties and heat source in order to control temperature patterns.
基金by National Natural Science Foundation of China and the Natural Sclence Foundation of Shandong Province of China
文摘In this paper,we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method,many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations,which contain solitary wave solutions,trigonometric function solutions,and rational solutions,are obtained.
文摘In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the fin heat dissipating capacity but the internal heat generation decreases the heat enhancement capacity of extended surface.Also,it is established that when the internal heat parameter increases to some certain values,some negative effects are recorded where the fin stores heat rather than dissipating it.This scenario defeats the prime purpose of the cooling fin.Additionally,it is established in the present study that the limiting value of porosity parameter for thermal stability for the passive device increases as internal heat parameter increases.This shows that although the internal heat parameter can help assist higher range and value of thermal stability of the fin,it produces negative effect which greatly defeats the ultimate purpose of the fin.The results in the work will help in fin design for industrial applications where internal heat generation is involved.
文摘In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This semi-analytic method has the advantage of overcoming the obstacle of the hardest nonlinear terms and is used to explain the origin of the bright and dark soliton solutions through the Schrödinger equation in its non-local form and the Radhakrishnan-Kundu-Laksmannan (RKL) equation. Numerical examples demonstrate the effectiveness of this method.
文摘The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.
基金supported by National Key R&D Program of China(2022YFC3104200)the China Postdoctoral Science Foundation(2023M742157)+3 种基金the Shandong Province Taishan Scholars Project(tsqn201909172)the Shandong Provincial Natural Science Foundation(ZR2023QA097)the Open Research Fund Program of State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology(LP2309)the Innovation Project of Qingdao Post-Doctoral(QDBSH20230202121).
文摘Through active manipulation of wavelengths,a structure exposed to a water-wave field can achieve a target hydrodynamic performance.Based on the form invariance of the governing equation for shallow water waves,wavelength modulators have been proposed using the space transformation method,which enables wavelength manipulation by distributing an anisotropic medium that incorporates water depth and gravitational acceleration within the modulation space.First,annular wavelength modulators were designed using the space transformation method to reduce or amplify the wavelength of shallow water waves.The control method of wavelength scaling ratios was investigated.In addition to plane waves,the wavelength modulator was applied to manipulate the wavelength of cylindrical waves.Furthermore,the interactions between a vertical cylinder and modulated water waves were studied.Results indicate that the wavelength can be arbitrarily reduced or amplified by adjusting the dimensional parameters of the modulator.Additionally,the modulator is effective for plane waves and cylindrical waves.This wavelength modulator can enable the structure to achieve the desired scattering characteristics at the target wavelength.
文摘Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a number of track parameters.One possible reason for deviations between simulated and measured results for the dynamic track behaviour is the uncertainty of the value of some track parameters used as input for the simulation.This in turn results in an uncertainty in the simulation results.In this contribution,it is proposed to use the general transformation method to assess a uncertainty band for the results.Most relevant input parameters for determining the point input mobility and the track decay rate for a ballasted track are analysed with regard to the uncertainties and for the value of each an interval is determined.Then,the general transformation method is applied to four different simulation methods,working both in the frequency and time domains.For one example track,the resulting uncertainty bands are compared to one dataset with measurements for the point mobility and the track decay rate.In addition,a sensitivity analysis is performed to determine the parameters that significantly influence the overall result.While all four simulation methods produce broad uncertainty bands for the results,none did match the measured results for the point mobility and the track decay rate over the entire frequency range considered.Besides the large influence of the uncertain pad stiffness,it turned out that the rail wear is also a significant source of uncertainty of the results.Overall,it is demonstrated that the proposed approach allows assessing the influence of uncertain input parameters in detail.
基金Supported by Special Foundation of President of Guangdong Academy of Agricultural Sciences(201217)
文摘At present, transgenic technologies have become important means of plant breeding, and the application and promotion of transgenic technologies have created huge economic and social benefits. Transgenic plant products have significantly affected human life. Anthurium andraeanum is the second major tropical potted flower and its transgenic breeding has a promising prospect of application. In this paper, acceptors, transformation methods and introduced exogenous genes （ including reporter genes, selectable marker genes and target genes） of Anthurium andraeanum were summarized; in addition, several issues related to transforma- tion of Anthurium andraeanum were analyzed, aiming at providing reference for transgenic breeding of Anthurium andraeanum.
基金supported by National Natural Science Foundation of China(Grant No.51075327)National Key Basic Research and Development Program of China(973 Program,Grant No.2013CB035705)+3 种基金Shaanxi Provincial Natural Science Foundation of China(Grant No.2013JQ7008)Open Project of State Key Laboratory of Mechanical Transmission of China(Grant No.SKLMT-KFKT-201011)Tribology Science Fund of State Key Laboratory of Tribology of China(Grant No.SKLTKF11A02)Scientific Research Program of Shaanxi Provincial Education Department of China(Grant Nos.12JK0661,12JK0680)
文摘Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy,low friction,low noise and high stability.The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system.The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail.The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory.A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing.The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method.The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system,and the dynamic equation of motion is calculated by the modified Wilson-0-based method.To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings,such as bifurcation and chaos,the bifurcation diagram,the orbit diagram,the Poincar6 map,the time series and the frequency spectrum are employed.The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena,such as the periodic,period-doubling,quasi-periodic,period-4 and chaotic motion,and so on.The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.
文摘Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytically using differential transformation method. Velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are determined analytically. The influence of pertinent parameters such as magnetic parameter, nanofluid volume fraction, viscosity parameter and Eckert number on the flow and heat transfer characteristics is discussed. Results indicate that skin friction coefficient decreases with increase of magnetic parameter, nanofluid volume fraction and viscosity parameter. Nusselt number increases with increase of magnetic parameter and nanofluid volume fraction while it decreases with increase of Eckert number and viscosity parameter.
文摘The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more practical results, this study considers a cubic polynomial relationship between the humidity ratio of saturated air and the corresponding fin surface temperature. The temperature distribution has been determined by solving the highly non-linear governing equations using a semi-analytical transformation technique called Differential Transform Method. A comparison of the results with that of a numerical model shows that this transformation method is a very efficient and convenient tool for solution of non-linear problems. The effects of various geometric, thermo-physical and psychometric parameters on the temperature distribution, fin efficiency and optimum design condition have been investigated. Also, a comparison has been presented between solid and porous fins and the results point out that by selecting an appropriate value of porosity, the heat transfer rate can be increased than the corresponding solid fin.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
文摘We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.
基金funded by“Taif University Researchers Supporting Project Number(TURSP-2020/16),Taif University,Taif,Saudi Arabia.”。
文摘The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.
基金financially supported by the Chinese State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(Grant No.GKZD010038)
文摘This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.
