This study aims to elucidate the connection between the shape factor of GO(graphene oxide)nanoparticles and the behavior of blood-based non-aligned,2-dimensional,incompressible nanofluid flow near stagnation point,und...This study aims to elucidate the connection between the shape factor of GO(graphene oxide)nanoparticles and the behavior of blood-based non-aligned,2-dimensional,incompressible nanofluid flow near stagnation point,under the influence of temperature-dependent viscosity.Appropriate similarity transformations are employed to transform the non-linear partial differential equations(PDEs)into ordinary differential equations(ODEs).The governing equations are subsequently resolved by utilizing the shooting method.The modified Maxwell model is used to estimate the thermal efficiency of the nanofluid affected by different nanoparticle shapes.The impact of various shapes of GO nanoparticles on the velocity and temperature profiles,along with drag forces and heat flux at the stretching boundary,are examined with particular attention to factors such as viscosity changes.Numerical findings are based on the constant concentration of ϕ=5% with nanoparticles measuring 25 nm in size.The influence of different shapes of GO nanoparticles is analyzed for velocity,temperature distributions,as well as drag forces,and heat transfer at the stretching boundary.The velocity profile is highest for spherical-shaped nanoparticles,whereas the blade-shaped particles produced the greatest temperature distribution.Additionally,itwas observed that enhancing the nanoparticles’volume fraction from 1%to 9%significantly improved the temperature profile.Streamline trends are more inclined to the left when the stretching ratio parameter B=0.7 is applied,and a similar pattern is noted for the variable viscosity case with m=0.5.Furthermore,the blade-shaped nanoparticles exhibit the highest thermal conductivity,while the spherical-shaped nanoparticles display the lowest.展开更多
In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T...In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).展开更多
This investigation describes the nanofluid flow in a non-Darcy porous medium between two stretching and rotating disks. A nanofluid comprises of nanoparticles of silver and copper. Water is used as a base fluid. Heat ...This investigation describes the nanofluid flow in a non-Darcy porous medium between two stretching and rotating disks. A nanofluid comprises of nanoparticles of silver and copper. Water is used as a base fluid. Heat is being transferred with thermal radiation and the Joule heating. A system of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are obtained. Effects of various parameters are analyzed for the velocity and temperature. Numerical values of the skin friction coefficient and the Nusselt number are tabulated and examined. It can be seen that the radial velocity is affected in the same manner with both porous and local inertial parameters. A skin friction coefficient depicts the same impact on both disks for both nanofluids with larger stretching parameters.展开更多
In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sy...In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.展开更多
The purpose of this paper is to establish a formula of higher derivative by Faà di Bruno formula, and apply it to some known results to get some identities involving complete Bell polynomials.
In recent years,physical informed neural networks(PINNs)have been shown to be a powerful tool for solving PDEs empirically.However,numerical analysis of PINNs is still missing.In this paper,we prove the convergence ra...In recent years,physical informed neural networks(PINNs)have been shown to be a powerful tool for solving PDEs empirically.However,numerical analysis of PINNs is still missing.In this paper,we prove the convergence rate to PINNs for the second order elliptic equations with Dirichlet boundary condition,by establishing the upper bounds on the number of training samples,depth and width of the deep neural networks to achieve desired accuracy.The error of PINNs is decomposed into approximation error and statistical error,where the approximation error is given in C2 norm with ReLU^(3)networks(deep network with activation function max{0,x^(3)})and the statistical error is estimated by Rademacher complexity.We derive the bound on the Rademacher complexity of the non-Lipschitz composition of gradient norm with ReLU^(3)network,which is of immense independent interest.展开更多
For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessa...For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.展开更多
We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integra...We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integral operators,which leads to a non-Hermitian generalized matrix eigenvalue problems.The spectral indicator method(SIM)is then applied to calculate the(complex)eigenvalues.The convergence is proved using the spectral approximation theory for(non-selfadjoint)compact operators.Numerical examples are presented for validation.展开更多
In this paper,a new earthquake location method based on the waveform inversion is proposed.As is known to all,the waveform misfit function under the L2 measure is suffering from the cycle skipping problem.This leads t...In this paper,a new earthquake location method based on the waveform inversion is proposed.As is known to all,the waveform misfit function under the L2 measure is suffering from the cycle skipping problem.This leads to a very small convergence domain of the conventional waveform based earthquake location methods.In present study,by introducing and solving two simple sub-optimization problems,we greatly expand the convergence domain of the waveform based earthquake location method.According to a large number of numerical experiments,the new method expands the range of convergence by several tens of times.This allows us to locate the earthquake accurately even from some relatively bad initial values.展开更多
Understanding the near boundary acoustic oscillation of microbubbles is critical for the effective design of ultrasonic biomedical devices and surface cleaning technologies.Accordingly,this study investigates the thre...Understanding the near boundary acoustic oscillation of microbubbles is critical for the effective design of ultrasonic biomedical devices and surface cleaning technologies.Accordingly,this study investigates the three-dimensional microbubble oscillation between two curved rigid plates experiencing a planar acoustic field using boundary integral method(BIM).The numerical model is validated via comparison with the nonlinear oscillation of the bubble governed by the modified Rayleigh-Plesset equation and with the axisymmetric model for an acoustic microbubble in infinite fluid domain.Then,the influence of the wave direction and horizontal standoff distance(h)on the bubble dynamics(including jet velocity,jet direction,centroid movement,total energy,and Kelvin impulse)were evaluated.It was concluded that the jet velocity,the maximum radius and the total energy of the bubble are not significantly influenced by the wave direction,while the jet direction and the high-pressure region depend strongly on it.More importantly,it was found that the jet velocity and the high-pressure region around the jet in acoustic bubble are drastically larger than their counterparts in the gas bubble.展开更多
This paper is concerned with numerical solutions of the LDG method for 1D wave equations.Superconvergence and energy conserving properties have been studied.We first study the superconvergence phenomenon for linear pr...This paper is concerned with numerical solutions of the LDG method for 1D wave equations.Superconvergence and energy conserving properties have been studied.We first study the superconvergence phenomenon for linear problems when alternating fluxes are used.We prove that,under some proper initial discretization,the numerical trace of the LDG approximation at nodes,as well as the cell average,converge with an order 2k+1.In addition,we establish k+2-th order and k+1-th order superconvergence rates for the function value error and the derivative error at Radau points,respectively.As a byproduct,we prove that the LDG solution is superconvergent with an order k+2 towards the Radau projection of the exact solution.Numerical experiments demonstrate that in most cases,our error estimates are optimal,i.e.,the error bounds are sharp.In the second part,we propose a fully discrete numerical scheme that conserves the discrete energy.Due to the energy conserving property,after long time integration,our method still stays accurate when applied to nonlinear Klein-Gordon and Sine-Gordon equations.展开更多
In this paper,the author considers a class of complete noncompact Riemannian manifoldswhich satisfy certain conditions on Ricci curvature and volume comparison. It is shown thatany harmonic map with finite energy from...In this paper,the author considers a class of complete noncompact Riemannian manifoldswhich satisfy certain conditions on Ricci curvature and volume comparison. It is shown thatany harmonic map with finite energy from such a manifold M into a normal geodesic ball inanother manifold N must be asymptotically constant at the infinity of each large end of M. Arelated existence theorem for harmonic maps is established.展开更多
In this paper, we study the generalized Riemann problem for a scalar Chapman-Jouguet combustion model in a neighborhood of the origin on upper half of the （x, t）plane. We focus our attention on the perturbation on i...In this paper, we study the generalized Riemann problem for a scalar Chapman-Jouguet combustion model in a neighborhood of the origin on upper half of the （x, t）plane. We focus our attention on the perturbation on initial binding energy. Under the entropy conditions, the solutions are obtained constructively. It shows that the perturbed Riemann solutions possess the structural stability except the case that the corresponding Riemann solutions contain CJDT, for which CJDT may transform into SDT after perturbation on initial binding energy in the neighborhood of the origin.展开更多
How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of f...How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.展开更多
A new method of the reproducing kernel Hilbert space is applied to a twodimensional parabolic inverse source problem with the final overdetermination. The exact and approximate solutions are both obtained in a reprodu...A new method of the reproducing kernel Hilbert space is applied to a twodimensional parabolic inverse source problem with the final overdetermination. The exact and approximate solutions are both obtained in a reproducing kernel space. The approximate solution and its partial derivatives are proved to converge to the exact solution and its partial derivatives, respectively. A technique is proposed to improve some existing methods. Numerical results show that the method is of high precision, and confirm the robustness of our method for reconstructing source parameter.展开更多
We show how to apply convolution quadrature(CQ)to approximate the time domain electric field integral equation(EFIE)for electromagnetic scattering.By a suitable choice of CQ,we prove that the method is unconditionally...We show how to apply convolution quadrature(CQ)to approximate the time domain electric field integral equation(EFIE)for electromagnetic scattering.By a suitable choice of CQ,we prove that the method is unconditionally stable and has the optimal order of convergence.Surprisingly,the resulting semi discrete EFIE is dispersive and dissipative,and we analyze this phenomena.Finally,we present numerical results supporting and extending our convergence analysis.展开更多
In this paper we prove first the existence and uniqueness results for the weak solution,to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition;th...In this paper we prove first the existence and uniqueness results for the weak solution,to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition;then we study the asymptotic analysis when one dimension of the fluid domain tend to zero.The strong convergence of the velocity is proved,a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.展开更多
文摘This study aims to elucidate the connection between the shape factor of GO(graphene oxide)nanoparticles and the behavior of blood-based non-aligned,2-dimensional,incompressible nanofluid flow near stagnation point,under the influence of temperature-dependent viscosity.Appropriate similarity transformations are employed to transform the non-linear partial differential equations(PDEs)into ordinary differential equations(ODEs).The governing equations are subsequently resolved by utilizing the shooting method.The modified Maxwell model is used to estimate the thermal efficiency of the nanofluid affected by different nanoparticle shapes.The impact of various shapes of GO nanoparticles on the velocity and temperature profiles,along with drag forces and heat flux at the stretching boundary,are examined with particular attention to factors such as viscosity changes.Numerical findings are based on the constant concentration of ϕ=5% with nanoparticles measuring 25 nm in size.The influence of different shapes of GO nanoparticles is analyzed for velocity,temperature distributions,as well as drag forces,and heat transfer at the stretching boundary.The velocity profile is highest for spherical-shaped nanoparticles,whereas the blade-shaped particles produced the greatest temperature distribution.Additionally,itwas observed that enhancing the nanoparticles’volume fraction from 1%to 9%significantly improved the temperature profile.Streamline trends are more inclined to the left when the stretching ratio parameter B=0.7 is applied,and a similar pattern is noted for the variable viscosity case with m=0.5.Furthermore,the blade-shaped nanoparticles exhibit the highest thermal conductivity,while the spherical-shaped nanoparticles display the lowest.
基金Supported by the NSF of China(10371106,60774073)
文摘In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).
文摘This investigation describes the nanofluid flow in a non-Darcy porous medium between two stretching and rotating disks. A nanofluid comprises of nanoparticles of silver and copper. Water is used as a base fluid. Heat is being transferred with thermal radiation and the Joule heating. A system of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are obtained. Effects of various parameters are analyzed for the velocity and temperature. Numerical values of the skin friction coefficient and the Nusselt number are tabulated and examined. It can be seen that the radial velocity is affected in the same manner with both porous and local inertial parameters. A skin friction coefficient depicts the same impact on both disks for both nanofluids with larger stretching parameters.
文摘In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.
基金Supported by the National Natural Science Foundation of China(Grant No.11601543,No.11601216,11701257)Supported by the NSF of Henan Province under Grant(No.172102410069)+1 种基金Supported by the NSF of Education Bureau of Henan Province under Grant(No.16B110009,18A110025)Supported by the Youth Foundation of Luoyang Normal university under Grant(No.2013-QNJJ-001)
文摘The purpose of this paper is to establish a formula of higher derivative by Faà di Bruno formula, and apply it to some known results to get some identities involving complete Bell polynomials.
基金supported by the National Key Research and Development Program of China(No.2020YFA0714200)the National Science Foundation of China(No.12125103,No.12071362,No.11971468,No.11871474,No.11871385)+1 种基金the Natural Science Foundation of Hubei Province(No.2021AAA010,No.2019CFA007)the Fundamental Research Funds for the Central Universities.
文摘In recent years,physical informed neural networks(PINNs)have been shown to be a powerful tool for solving PDEs empirically.However,numerical analysis of PINNs is still missing.In this paper,we prove the convergence rate to PINNs for the second order elliptic equations with Dirichlet boundary condition,by establishing the upper bounds on the number of training samples,depth and width of the deep neural networks to achieve desired accuracy.The error of PINNs is decomposed into approximation error and statistical error,where the approximation error is given in C2 norm with ReLU^(3)networks(deep network with activation function max{0,x^(3)})and the statistical error is estimated by Rademacher complexity.We derive the bound on the Rademacher complexity of the non-Lipschitz composition of gradient norm with ReLU^(3)network,which is of immense independent interest.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10831003 and 10771196）
文摘For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.
文摘We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integral operators,which leads to a non-Hermitian generalized matrix eigenvalue problems.The spectral indicator method(SIM)is then applied to calculate the(complex)eigenvalues.The convergence is proved using the spectral approximation theory for(non-selfadjoint)compact operators.Numerical examples are presented for validation.
基金This work was supported by the National Nature Science Foundation of China(Grant Nos.41230210,41390452)Hao Wu was also partially supported by the National Nature Science Foundation of China(Grant Nos.11101236,91330203)and SRF for ROCS,SEM.The authors are grateful to Prof.Shi Jin for his helpful suggestions and discussions that greatly improve the presentation.Hao Wu would like to thank Prof.Ping Tong for his valuable comments.The authors would also like to thank the referees for their valuable suggestions which helped to improve the content and presentation of this paper.
文摘In this paper,a new earthquake location method based on the waveform inversion is proposed.As is known to all,the waveform misfit function under the L2 measure is suffering from the cycle skipping problem.This leads to a very small convergence domain of the conventional waveform based earthquake location methods.In present study,by introducing and solving two simple sub-optimization problems,we greatly expand the convergence domain of the waveform based earthquake location method.According to a large number of numerical experiments,the new method expands the range of convergence by several tens of times.This allows us to locate the earthquake accurately even from some relatively bad initial values.
文摘Understanding the near boundary acoustic oscillation of microbubbles is critical for the effective design of ultrasonic biomedical devices and surface cleaning technologies.Accordingly,this study investigates the three-dimensional microbubble oscillation between two curved rigid plates experiencing a planar acoustic field using boundary integral method(BIM).The numerical model is validated via comparison with the nonlinear oscillation of the bubble governed by the modified Rayleigh-Plesset equation and with the axisymmetric model for an acoustic microbubble in infinite fluid domain.Then,the influence of the wave direction and horizontal standoff distance(h)on the bubble dynamics(including jet velocity,jet direction,centroid movement,total energy,and Kelvin impulse)were evaluated.It was concluded that the jet velocity,the maximum radius and the total energy of the bubble are not significantly influenced by the wave direction,while the jet direction and the high-pressure region depend strongly on it.More importantly,it was found that the jet velocity and the high-pressure region around the jet in acoustic bubble are drastically larger than their counterparts in the gas bubble.
基金This work is supported in part by the National Natural Science Foundation of China(NSFC)under grants Nos.11201161,11471031,11501026,91430216,U1530401China Postdoctoral Science Foundation under grant Nos.2015M570026,2016T90027the US National Science Foundation(NSF)through grant DMS-1419040。
文摘This paper is concerned with numerical solutions of the LDG method for 1D wave equations.Superconvergence and energy conserving properties have been studied.We first study the superconvergence phenomenon for linear problems when alternating fluxes are used.We prove that,under some proper initial discretization,the numerical trace of the LDG approximation at nodes,as well as the cell average,converge with an order 2k+1.In addition,we establish k+2-th order and k+1-th order superconvergence rates for the function value error and the derivative error at Radau points,respectively.As a byproduct,we prove that the LDG solution is superconvergent with an order k+2 towards the Radau projection of the exact solution.Numerical experiments demonstrate that in most cases,our error estimates are optimal,i.e.,the error bounds are sharp.In the second part,we propose a fully discrete numerical scheme that conserves the discrete energy.Due to the energy conserving property,after long time integration,our method still stays accurate when applied to nonlinear Klein-Gordon and Sine-Gordon equations.
文摘In this paper,the author considers a class of complete noncompact Riemannian manifoldswhich satisfy certain conditions on Ricci curvature and volume comparison. It is shown thatany harmonic map with finite energy from such a manifold M into a normal geodesic ball inanother manifold N must be asymptotically constant at the infinity of each large end of M. Arelated existence theorem for harmonic maps is established.
文摘In this paper, we study the generalized Riemann problem for a scalar Chapman-Jouguet combustion model in a neighborhood of the origin on upper half of the （x, t）plane. We focus our attention on the perturbation on initial binding energy. Under the entropy conditions, the solutions are obtained constructively. It shows that the perturbed Riemann solutions possess the structural stability except the case that the corresponding Riemann solutions contain CJDT, for which CJDT may transform into SDT after perturbation on initial binding energy in the neighborhood of the origin.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135,11471136the UIC Grant R201409+1 种基金the Zhuhai Premier Discipline Grantthe Self-Determined Research Funds of CCNU from the Colleges Basic Research and Operation of MOE under Grant Nos.CCNU14A05041,CCNU16A02012
文摘How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.
基金supported by the National Natural Science Foundation of China(No.91230119)
文摘A new method of the reproducing kernel Hilbert space is applied to a twodimensional parabolic inverse source problem with the final overdetermination. The exact and approximate solutions are both obtained in a reproducing kernel space. The approximate solution and its partial derivatives are proved to converge to the exact solution and its partial derivatives, respectively. A technique is proposed to improve some existing methods. Numerical results show that the method is of high precision, and confirm the robustness of our method for reconstructing source parameter.
基金funding this research under grant number DMS-0811104.
文摘We show how to apply convolution quadrature(CQ)to approximate the time domain electric field integral equation(EFIE)for electromagnetic scattering.By a suitable choice of CQ,we prove that the method is unconditionally stable and has the optimal order of convergence.Surprisingly,the resulting semi discrete EFIE is dispersive and dissipative,and we analyze this phenomena.Finally,we present numerical results supporting and extending our convergence analysis.
文摘In this paper we prove first the existence and uniqueness results for the weak solution,to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition;then we study the asymptotic analysis when one dimension of the fluid domain tend to zero.The strong convergence of the velocity is proved,a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.
