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 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
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
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
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
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
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
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
Corrosion re sistance of Zircaloy-4 alloy tube in superheated steam at 673 K/10.3 MPa is anisotropic.A part of the surface undergoes uniform corrosion while the other suffers nodular corrosion.Narrow and wide nodules ...Corrosion re sistance of Zircaloy-4 alloy tube in superheated steam at 673 K/10.3 MPa is anisotropic.A part of the surface undergoes uniform corrosion while the other suffers nodular corrosion.Narrow and wide nodules are observed after an exposure period of 3 and 30 days,respectively.A new matrix transformation method is established in order to study the formation mechanism of nodules in the cross-section(CS) of Zircaloy-4 alloy tube using the EBSD technique,while the CS perpendicular to axial direction(AD).The results reveal that the microtexture is a key factor behind the two types of corrosion.Furthermore,the oxide layers grow anisotropically over the corroded surface.A thick oxide layer forms over the nodular corrosion region on the grains with c-axis oriented in the range of 40° around tangential direction(TD),whereas a thin oxide layer over the uniform corrosion region is detected on the grains with c-axis oriented in the range of 68° around TD.In short,the anisotropic growth of oxide layer was caused by the change of microtexture of the Zr-4 alloy tube,and this anisotropic growth of oxide layer contributed to the nodules formation.展开更多
Diapycnal mixing plays an important role in the ocean circulation.Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy.Difficulty in obtaining eigen solutions of i...Diapycnal mixing plays an important role in the ocean circulation.Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy.Difficulty in obtaining eigen solutions of internal waves over curved topography is a limitation for further theoretical study on the generation problem and scattering process.In this study,a kind of transform method is put forward to derive the eigen solutions of internal waves over subcritical topography in twodimensional and linear framework.The transform converts the curved topography in physical space to flat bottom in transform space while the governing equation of internal waves is still hyperbolic if proper transform function is selected.Thus,one can obtain eigen solutions of internal waves in the transform space.Several examples of transform functions,which convert the linear slope,the convex slope,and the concave slope to flat bottom,and the corresponding eigen solutions are illustrated.A method,using a polynomial to approximate the transform function and least squares method to estimate the undetermined coefficients in the polynomial,is introduced to calculate the approximate expression of the transform function for the given subcritical topography.展开更多
The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD bo...The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.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
Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in...Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deforma- tion of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.展开更多
The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, a...The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.展开更多
Aiming at the existing problems of discrete cosine transform(DCT) de-noising method, we introduce the idea of wavelet neighboring coefficients(WNC) de-noising method, and propose the cosine neighboring coefficients(CN...Aiming at the existing problems of discrete cosine transform(DCT) de-noising method, we introduce the idea of wavelet neighboring coefficients(WNC) de-noising method, and propose the cosine neighboring coefficients(CNC) de-noising method. Based on DCT, a novel method for the fault feature extraction of hydraulic pump is analyzed. The vibration signal of pump is de-noised with CNC de-noising method, and the fault feature is extracted by performing Hilbert-Huang transform(HHT) to the output signal. The analysis results of the simulation signal and the actual one demonstrate that the proposed CNC de-noising method and the fault feature extraction method have more superior ability than the traditional ones.展开更多
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.
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 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.
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.
文摘Corrosion re sistance of Zircaloy-4 alloy tube in superheated steam at 673 K/10.3 MPa is anisotropic.A part of the surface undergoes uniform corrosion while the other suffers nodular corrosion.Narrow and wide nodules are observed after an exposure period of 3 and 30 days,respectively.A new matrix transformation method is established in order to study the formation mechanism of nodules in the cross-section(CS) of Zircaloy-4 alloy tube using the EBSD technique,while the CS perpendicular to axial direction(AD).The results reveal that the microtexture is a key factor behind the two types of corrosion.Furthermore,the oxide layers grow anisotropically over the corroded surface.A thick oxide layer forms over the nodular corrosion region on the grains with c-axis oriented in the range of 40° around tangential direction(TD),whereas a thin oxide layer over the uniform corrosion region is detected on the grains with c-axis oriented in the range of 68° around TD.In short,the anisotropic growth of oxide layer was caused by the change of microtexture of the Zr-4 alloy tube,and this anisotropic growth of oxide layer contributed to the nodules formation.
基金the National Nature Science Foundation of China under contract No. 40876015the National High Technology Research and Development Program of China (863 Program) under contract No. 2008AA09A402
文摘Diapycnal mixing plays an important role in the ocean circulation.Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy.Difficulty in obtaining eigen solutions of internal waves over curved topography is a limitation for further theoretical study on the generation problem and scattering process.In this study,a kind of transform method is put forward to derive the eigen solutions of internal waves over subcritical topography in twodimensional and linear framework.The transform converts the curved topography in physical space to flat bottom in transform space while the governing equation of internal waves is still hyperbolic if proper transform function is selected.Thus,one can obtain eigen solutions of internal waves in the transform space.Several examples of transform functions,which convert the linear slope,the convex slope,and the concave slope to flat bottom,and the corresponding eigen solutions are illustrated.A method,using a polynomial to approximate the transform function and least squares method to estimate the undetermined coefficients in the polynomial,is introduced to calculate the approximate expression of the transform function for the given subcritical topography.
基金supported by the National Natural Science Foundation of China (Nos. 50936003 and 51076012)the Open Project of State Key Laboratory for Advanced Metals and Materials (No. 2009Z-02)
文摘The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.
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.
基金supported by the National Natural Science Foundation of China (10472004)
文摘Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deforma- tion of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.
基金Project supported by the DST-FIST Program for Higher Education Institutions of India(No. SR/FST/MS-I/2018/23(C))。
文摘The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.
基金the National Natural Science Foundation of China(No.51275524)the General Armaments Department Equipment Support Research Project
文摘Aiming at the existing problems of discrete cosine transform(DCT) de-noising method, we introduce the idea of wavelet neighboring coefficients(WNC) de-noising method, and propose the cosine neighboring coefficients(CNC) de-noising method. Based on DCT, a novel method for the fault feature extraction of hydraulic pump is analyzed. The vibration signal of pump is de-noised with CNC de-noising method, and the fault feature is extracted by performing Hilbert-Huang transform(HHT) to the output signal. The analysis results of the simulation signal and the actual one demonstrate that the proposed CNC de-noising method and the fault feature extraction method have more superior ability than the traditional ones.
