The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenva...The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.展开更多
Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated ...In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.展开更多
The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact soluti...The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.展开更多
The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for...The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.展开更多
The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell(UCM)fluid between parallel plates.The lower plate is porous and s...The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell(UCM)fluid between parallel plates.The lower plate is porous and stationary,while the top plate is impermeable and moving.The equations that describe the flow are transformed into non-linear ordinary differential equations with boundary conditions by employing similarity transformations.The Homotopy Perturbation Method(HPM)is then employed to approach the obtained non-linear ordinary differential equations and get an approximate analytical solution.The analysis includes plotting the velocity profile for different Reynolds number values and temperature distribution curves for distinct physical parameters such as Reynolds number,Deborah number,magnetic parameter,porosity parameter,radiation parameter,and Prandtl number.In the case of injection,the temporal profile declines with an increase in radiation parameter as the plates move away from each other,and an opposite trend is observed as plates move towards each other.Furthermore,the skin friction coefficient and heat transfer rate are analysed for the impact of these parameters using HPM.The numerical values obtained using HPM are compared using the classical finite difference method.The results show good agreement between the semi-analytical and numerical solutions.展开更多
The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy ...The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method展开更多
A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using su...A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.展开更多
The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The govern...The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.展开更多
Squealer tip is widely used in turbines to reduce tip leakage loss.In typical turbine environment,the squealer tip leakage flow is affected by multiple factors such as the relative casing motion and the wide range of ...Squealer tip is widely used in turbines to reduce tip leakage loss.In typical turbine environment,the squealer tip leakage flow is affected by multiple factors such as the relative casing motion and the wide range of variable incidence angles.The development of experimental methods which can accurately model the real turbine environment and influencing factors is of great significance to study the squealer tip leakage flow mechanism.In the present paper,a low-speed turbine cascade test facility which can model the relative casing motion and wide range of variable incidence angles(-25°to 55°)is built.Based on the similarity criteria,a high-low speed similarity transformation method of the turbine cascade is established by considering the thickness of the turbine blade.A combined testing method of Particle Image Velocimetry(PIV)and local pressure measurement is proposed to obtain the complex flow structures within the tip cavity.The results show that the experimental method can successfully model the relative casing motion and the wide range of variable incidence angles.The low-speed cascade obtained by the similarity transformation can model the high-speed flow accurately.The measurement technique developed can obtain the complex flow field and successfully capture the scraping vortex within the squealer tip.展开更多
Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeabili...Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.展开更多
We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by usin...We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.展开更多
Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transforma...Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.展开更多
With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction,...With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.展开更多
This article aims to investigate the Darcy Forchhemier mixed convection flow of the hybrid nanofluid through an inclined extending cylinder.Two different nanoparticles such as carbon nanotubes(CNTs)and iron oxide Fe3O...This article aims to investigate the Darcy Forchhemier mixed convection flow of the hybrid nanofluid through an inclined extending cylinder.Two different nanoparticles such as carbon nanotubes(CNTs)and iron oxide Fe3O4 have been added to the base fluid in order to prepare a hybrid nanofluid.Nonlinear partial differential equations for momentum,energy and convective diffusion have been changed into dimensionless ordinary differential equations after using Von Karman approach.Homotopy analysis method(HAM),a powerful analytical approach has been used to find the solution to the given problem.The effects of the physical constraints on velocity,concentration and temperature profile have been drawn as well for discussion purpose.The numerical outcomes have been carried out for the drag force,heat transfer rate and diffusion rate etc.The Biot number of heat and mass transfer affects the fluid temperature whereas the Forchhemier parameter and the inclination angle decrease the velocity of the fluid flow.The results show that hybrid nanofluid is the best source of enhancing heat transfer and can be used for cooling purposes as well.展开更多
Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifie...Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.展开更多
The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstl...The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.展开更多
A method of shape encoding and retrieval is proposed in this letter, which uses centripetal code to encode shape and extracts shape's convex for retrieval. For the rotation invariance and translation invariance of...A method of shape encoding and retrieval is proposed in this letter, which uses centripetal code to encode shape and extracts shape's convex for retrieval. For the rotation invariance and translation invariance of the centripetal code and the normalization of convex,the proposed retrieval method is similarity transform resistant, Experimental results confirm this capability.展开更多
In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the...In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.展开更多
The purpose of this paper is to construct an orthogonal Armlet multi-wavelets with mul-tiplicity r and dilation factor a.Firstly,the definition of Armlets with dilation factor a is proposed in this paper.Based on the ...The purpose of this paper is to construct an orthogonal Armlet multi-wavelets with mul-tiplicity r and dilation factor a.Firstly,the definition of Armlets with dilation factor a is proposed in this paper.Based on the Two-scale Similar Transform(TST),the notion of the Para-unitary A-scale Similar Transform(PAST) is introduced,and we also give the transform on the all two-scale matrix symbols of the multi-wavelets with dilation a.Then we show that the PAST and the transform on the matrix symbols of the multi-wavelets keep the orthogonality of the multi-wavelets system.We discuss the condition that multi-wavelets corresponding to the multi-scaling functions are all Armlets.After performing the PAST and the transform on the matrix symbols of the multi-wavelets,the multi-scaling function can be balanced and the corresponding multi-wavelets can be Armlets at the same time.The construction of Armlets with high order is also discussed.At last,by a given example,we can conclude that the algorithm is feasible and efficient.展开更多
文摘The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.
文摘Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
文摘In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.
基金Xi’an University of Architecture and Technology(Grant no.002/2040221134).
文摘The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.
文摘The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.
文摘The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell(UCM)fluid between parallel plates.The lower plate is porous and stationary,while the top plate is impermeable and moving.The equations that describe the flow are transformed into non-linear ordinary differential equations with boundary conditions by employing similarity transformations.The Homotopy Perturbation Method(HPM)is then employed to approach the obtained non-linear ordinary differential equations and get an approximate analytical solution.The analysis includes plotting the velocity profile for different Reynolds number values and temperature distribution curves for distinct physical parameters such as Reynolds number,Deborah number,magnetic parameter,porosity parameter,radiation parameter,and Prandtl number.In the case of injection,the temporal profile declines with an increase in radiation parameter as the plates move away from each other,and an opposite trend is observed as plates move towards each other.Furthermore,the skin friction coefficient and heat transfer rate are analysed for the impact of these parameters using HPM.The numerical values obtained using HPM are compared using the classical finite difference method.The results show good agreement between the semi-analytical and numerical solutions.
文摘The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method
基金UGC,New Delhi,India under the Special Assistance Programme DSA Phase-1
文摘A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.
文摘The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.
基金supported by the National Natural Science Foundation of China(No.51676005)。
文摘Squealer tip is widely used in turbines to reduce tip leakage loss.In typical turbine environment,the squealer tip leakage flow is affected by multiple factors such as the relative casing motion and the wide range of variable incidence angles.The development of experimental methods which can accurately model the real turbine environment and influencing factors is of great significance to study the squealer tip leakage flow mechanism.In the present paper,a low-speed turbine cascade test facility which can model the relative casing motion and wide range of variable incidence angles(-25°to 55°)is built.Based on the similarity criteria,a high-low speed similarity transformation method of the turbine cascade is established by considering the thickness of the turbine blade.A combined testing method of Particle Image Velocimetry(PIV)and local pressure measurement is proposed to obtain the complex flow structures within the tip cavity.The results show that the experimental method can successfully model the relative casing motion and the wide range of variable incidence angles.The low-speed cascade obtained by the similarity transformation can model the high-speed flow accurately.The measurement technique developed can obtain the complex flow field and successfully capture the scraping vortex within the squealer tip.
基金supported by the National Natural Science Foundation of China(11102237)Program for Changjiang Scholars and Innovative Research Team in University(IRT1294)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20110133120012)China Scholarship Council(CSC)
文摘Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.
文摘We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10772110） and the Natural Science Foundation of Zhejiang Province, China （Grant Nos. Y606049, Y6090681, and Y6100257）.
文摘Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
基金Project supported by the National Natural Science Foundations of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers (Grant No. 2009RC01)the Scientific Research and Developed Fund of Zhejiang Agricultural and Forestry University,China (Grant No. 2009FK42)
文摘With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.
文摘This article aims to investigate the Darcy Forchhemier mixed convection flow of the hybrid nanofluid through an inclined extending cylinder.Two different nanoparticles such as carbon nanotubes(CNTs)and iron oxide Fe3O4 have been added to the base fluid in order to prepare a hybrid nanofluid.Nonlinear partial differential equations for momentum,energy and convective diffusion have been changed into dimensionless ordinary differential equations after using Von Karman approach.Homotopy analysis method(HAM),a powerful analytical approach has been used to find the solution to the given problem.The effects of the physical constraints on velocity,concentration and temperature profile have been drawn as well for discussion purpose.The numerical outcomes have been carried out for the drag force,heat transfer rate and diffusion rate etc.The Biot number of heat and mass transfer affects the fluid temperature whereas the Forchhemier parameter and the inclination angle decrease the velocity of the fluid flow.The results show that hybrid nanofluid is the best source of enhancing heat transfer and can be used for cooling purposes as well.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11772017,11272023,and 11471050the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11874324 and 11705164)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LY17A040011,LY17F050011,and LR20A050001)+1 种基金the Foundation of “New Century 151 Talent Engineering” of Zhejiang Province of Chinathe Youth Talent Program of Zhejiang A&F University
文摘The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.
基金National Natural Science Foundation of China(No. 60172045)863-306 Project (863-306-ZT03-09)
文摘A method of shape encoding and retrieval is proposed in this letter, which uses centripetal code to encode shape and extracts shape's convex for retrieval. For the rotation invariance and translation invariance of the centripetal code and the normalization of convex,the proposed retrieval method is similarity transform resistant, Experimental results confirm this capability.
文摘In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.
基金Supported by the Development Program for Young Teacher in the Science Researcher Project for Colleges and Universities of Xinjiang Province of China (No. XJEDU-2009S67)
文摘The purpose of this paper is to construct an orthogonal Armlet multi-wavelets with mul-tiplicity r and dilation factor a.Firstly,the definition of Armlets with dilation factor a is proposed in this paper.Based on the Two-scale Similar Transform(TST),the notion of the Para-unitary A-scale Similar Transform(PAST) is introduced,and we also give the transform on the all two-scale matrix symbols of the multi-wavelets with dilation a.Then we show that the PAST and the transform on the matrix symbols of the multi-wavelets keep the orthogonality of the multi-wavelets system.We discuss the condition that multi-wavelets corresponding to the multi-scaling functions are all Armlets.After performing the PAST and the transform on the matrix symbols of the multi-wavelets,the multi-scaling function can be balanced and the corresponding multi-wavelets can be Armlets at the same time.The construction of Armlets with high order is also discussed.At last,by a given example,we can conclude that the algorithm is feasible and efficient.
