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
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 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
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
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 the present paper a differential transformation method(DTM)is used to obtain the solution of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall.The comparis...In the present paper a differential transformation method(DTM)is used to obtain the solution of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall.The comparison between the results from the differential transfomiation method and numerical method are in well agreement which proofs the capability of this method for solving such problems.After this validity,results are investigated for the velocity and temperature for various values of Reynolds number,Prandtl number and power law index.展开更多
A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency ba...A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper＇s non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.展开更多
The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been s...The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.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, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.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
In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easi...In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.展开更多
Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process...Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.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
Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for examp...Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable.展开更多
An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with interm...An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.展开更多
An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of...An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact Dower series solution.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.
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.
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 the present paper a differential transformation method(DTM)is used to obtain the solution of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall.The comparison between the results from the differential transfomiation method and numerical method are in well agreement which proofs the capability of this method for solving such problems.After this validity,results are investigated for the velocity and temperature for various values of Reynolds number,Prandtl number and power law index.
基金supported by the National Natural Science Foundation of China(61271359,61071215)Suzhou Science and Technology Development Plan(SYG201001)Key Joint Laboratory of Soochow University and JieMei Biomedical Engineering Instrument
文摘A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper＇s non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.
基金supported by the National Natural Science Foundation of China (90916007 and 91116008)
文摘The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.
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Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.
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.
文摘In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.
基金the National High.Technology Research and Development Programme of China(2004AA404013)
文摘Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.
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Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable.
基金Project supported by the National Basic Research Program of China(973 Program)(No.2011CB013800)
文摘An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.
基金Project supported by the National Natural Science Foundation of China(Nos.50909017,51109031, 50921001,11072053,and 51009022)the Doctoral Foundation of Ministry of Education of China(No.20100041120037)+1 种基金the Fundamental Research Funds for the Central Universities (Nos.DUT12LK52 and DUT12LK34)the Major State Basic Research Development Program of China(973 Program)(Nos.2010CB832704 and 2013CB036101)
文摘An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact Dower series solution.
