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 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
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
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
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 author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more...The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more fundamental interactions than the four, and these fundamental gauge fields are only components on the bottom manifold (i.e. our universe) projected by a unified gauge potential of the principal fiber bundle manifold;these components can satisfy the transformation of gauge potential, or even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, namely the generalized gauge equation expression, corresponding to gauge transformation invariance;so the invariance of gauge transformation is a necessary condition for unified field theory, and the four (or more) fundamental interaction fields of the universe are unified in a unified gauge field defined by the connection on the principal fiber bundle. In this paper, the author continues to propose a model of large-scale (gravitational) fundamental interactions in the universe based on the mathematical and physical picture of the principal fiber bundle, attempting to explain that dark matter and dark energy are merely reflections of these gravitational fundamental interactions that deviate in intensity from the gravitational fundamental interactions of the solar system at galaxy scales or some cosmic scales which are much larger than the solar system. All these “gravitational” fundamental interactions originate from the unified gauge field of the universe, namely the connection or curvature on the principal fiber bundle. These interactions are their projected representations on the bottom manifold (i.e. our universe) by different cross-sections (gauge transformations). These projection representations of the universe certainly are described by the generalized gauge equation or curvature similarity equation, and under the guidance of curvature gauge transformation factors, oscillate and evolve between the curvatures 1→0→-1→0→1 of the universe.展开更多
In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the s...In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.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
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
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
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
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
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
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
An unsteady viscous fluid flow with Dufour and Soret effect,which results in heat and mass transfer due to upward and downward motion of flexible rotating disk,has been studied.The upward or downward motion of non rot...An unsteady viscous fluid flow with Dufour and Soret effect,which results in heat and mass transfer due to upward and downward motion of flexible rotating disk,has been studied.The upward or downward motion of non rotating disk results in two dimensional flow,while the vertical action and rotation of the disk results in three dimensional flow.By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations.The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables.Then,we generalize the model by using the Caputo derivative.The numerical result for the fractional model is presented and validated with Runge Kutta order 4 method for classical case.The compared results are presented in Table and Figures.It is concluded that the fractional model is more realistic than that of classical one,because it simulates the fluid behavior at each fractional value rather than the integral values.展开更多
In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of...In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.展开更多
The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are ...The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are driven by the tangential motion of a bounding wall. The lid-driven cavity serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. This article presents a complete study of lid-driven cavity flows, with the primary focus being placed on the development of the flow when the Reynolds number was increased. In order to fully comprehend the physics of flow, it is necessary to take into consideration not only pure two-dimensional flows but also flows that are periodic in one space direction and the whole three-dimensional flow.展开更多
Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm...Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm,pulses in a blood vessel,or features in a circulatory system,this paper symbolically computes out an auto-B?cklund transformation via a noncharacteristic movable singular manifold,certain families of the solitonic solutions,as well as a family of the similarity reductions for a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers equation.Aiming,e.g.,at the dynamical radial displacement superimposed on the original static deformation from an arterial wall,our results rely on the axial stretch of the injured artery,blood as an incompressible Newtonian fluid,radius variation along the axial direction or aneurysmal geometry,viscosity of the fluid,thickness of the artery,mass density of the membrane material,mass density of the fluid,strain energy density of the artery,shear modulus,stretch ratio,etc.We also highlight that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.展开更多
Reliable transient thermal analysis plays a very important role in the engine safety analysis.Transient conjugate heat transfer simulation is an important way of temperature analysis.But there exists a great disparity...Reliable transient thermal analysis plays a very important role in the engine safety analysis.Transient conjugate heat transfer simulation is an important way of temperature analysis.But there exists a great disparity in the time scales between solid conduction and fluid convection.The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics.The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer.On the one hand,this method carries out a similar transformation on solid heat conduction,scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number.On the other hand,it takes very short time for the fluid domain to recover stability after a boundary disturbance.Based on the above characteristic,the flow time is directly compressed to the same as that of the solid domain.It is verified by Mark II vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction.In the situation of rapidly stable flow field,scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time.Within the application scope,the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.展开更多
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 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.
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.
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.
文摘The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more fundamental interactions than the four, and these fundamental gauge fields are only components on the bottom manifold (i.e. our universe) projected by a unified gauge potential of the principal fiber bundle manifold;these components can satisfy the transformation of gauge potential, or even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, namely the generalized gauge equation expression, corresponding to gauge transformation invariance;so the invariance of gauge transformation is a necessary condition for unified field theory, and the four (or more) fundamental interaction fields of the universe are unified in a unified gauge field defined by the connection on the principal fiber bundle. In this paper, the author continues to propose a model of large-scale (gravitational) fundamental interactions in the universe based on the mathematical and physical picture of the principal fiber bundle, attempting to explain that dark matter and dark energy are merely reflections of these gravitational fundamental interactions that deviate in intensity from the gravitational fundamental interactions of the solar system at galaxy scales or some cosmic scales which are much larger than the solar system. All these “gravitational” fundamental interactions originate from the unified gauge field of the universe, namely the connection or curvature on the principal fiber bundle. These interactions are their projected representations on the bottom manifold (i.e. our universe) by different cross-sections (gauge transformations). These projection representations of the universe certainly are described by the generalized gauge equation or curvature similarity equation, and under the guidance of curvature gauge transformation factors, oscillate and evolve between the curvatures 1→0→-1→0→1 of the universe.
基金The work is partially supported by the National Natural Science Foundation of China (No. 11801362).
文摘In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.
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.
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.
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.
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.
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.
文摘An unsteady viscous fluid flow with Dufour and Soret effect,which results in heat and mass transfer due to upward and downward motion of flexible rotating disk,has been studied.The upward or downward motion of non rotating disk results in two dimensional flow,while the vertical action and rotation of the disk results in three dimensional flow.By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations.The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables.Then,we generalize the model by using the Caputo derivative.The numerical result for the fractional model is presented and validated with Runge Kutta order 4 method for classical case.The compared results are presented in Table and Figures.It is concluded that the fractional model is more realistic than that of classical one,because it simulates the fluid behavior at each fractional value rather than the integral values.
基金Project supported by the Scientific Research Foundation of Lishui University,China (Grant No. KZ201110)
文摘In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.
文摘The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are driven by the tangential motion of a bounding wall. The lid-driven cavity serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. This article presents a complete study of lid-driven cavity flows, with the primary focus being placed on the development of the flow when the Reynolds number was increased. In order to fully comprehend the physics of flow, it is necessary to take into consideration not only pure two-dimensional flows but also flows that are periodic in one space direction and the whole three-dimensional flow.
基金supported by the National Natural Science Foundation of China under Grant Nos.11871116 and 11772017the Fundamental Research Funds for the Central Universities of China under Grant No.2019XD-A11.
文摘Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm,pulses in a blood vessel,or features in a circulatory system,this paper symbolically computes out an auto-B?cklund transformation via a noncharacteristic movable singular manifold,certain families of the solitonic solutions,as well as a family of the similarity reductions for a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers equation.Aiming,e.g.,at the dynamical radial displacement superimposed on the original static deformation from an arterial wall,our results rely on the axial stretch of the injured artery,blood as an incompressible Newtonian fluid,radius variation along the axial direction or aneurysmal geometry,viscosity of the fluid,thickness of the artery,mass density of the membrane material,mass density of the fluid,strain energy density of the artery,shear modulus,stretch ratio,etc.We also highlight that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.
基金This study was supported by major project of National Science Foundation of China(No.61890923).
文摘Reliable transient thermal analysis plays a very important role in the engine safety analysis.Transient conjugate heat transfer simulation is an important way of temperature analysis.But there exists a great disparity in the time scales between solid conduction and fluid convection.The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics.The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer.On the one hand,this method carries out a similar transformation on solid heat conduction,scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number.On the other hand,it takes very short time for the fluid domain to recover stability after a boundary disturbance.Based on the above characteristic,the flow time is directly compressed to the same as that of the solid domain.It is verified by Mark II vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction.In the situation of rapidly stable flow field,scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time.Within the application scope,the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.