： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati tech...： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The resu...By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.展开更多
Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equa...Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.展开更多
Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend...Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.展开更多
It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied,and the known results on the interface dynamics of this equation are under the compactly supported initial ...It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied,and the known results on the interface dynamics of this equation are under the compactly supported initial value.Moreover,there was no explicit formula regarding the interface due to the peculiarity of nonlocal dispersal operators.Anatural question is whether it is possible to provide a precise characterization of the interface with respect to small parameter for the general initial values(including exponentially bounded and unbounded).This paper is concerned with the interface dynamics of the nonlocal dispersal equation with scaling parameter.For the exponentially bounded initial value,by choosing the hyperbolic scaling,we show that at a very small time,the interface is confined within a generated layer whose thickness is at most O(√ɛ|ln ɛ|),,and subsequently,the interface propagates at a linear speed determined by the decay rate of initial value.For a class of exponentially unbounded initial value,by introducing the nonlinear scaling based on the decay of initial value,we deduce the corresponding Hamilton-Jacobi equation and describe precisely the propagation of the interface,which provides a superlinear speed of the interface.The investigation of the interface dynamics under different scaling reflects multiplex propagation modes in spatial dynamics and provides a new perspective on the wave propagation in nonlocal dispersal equations.展开更多
In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniq...In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniqueness results for steady symmetric transonic shock solutions to the nonisentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a symmetric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.展开更多
In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a b...In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.展开更多
The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These me...The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These methods allow to effectively suppress oscillations,including in velocity profiles,as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations.The methods can be applied both in explicit and implicit(method of separate sweeps)iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer,as well as in solving problems of magnetohydrodynamics and computational astrophysics.In order to avoid loss of solution accuracy on spatially non-uniform grids,in this work an algorithm of grid embeddings is developed,which is applied near transition points between cells of different sizes.The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes.Calculations are performed for the classical problem of decay of an arbitrary discontinuity(Sod’s problem)and the problem of propagation of two symmetric rarefaction waves in opposite directions(Einfeldt’s problem).In the case of using different methods for selecting the AAV,a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed.As a result of the comparative analysis,the applicability of these methods is shown in the spatially one-dimensional case(explicit and implicit iterative processes).The obtained results are compared with the data from the literature.The results coincide with analytical solutions with high accuracy,where the relative error does not exceed 0.1%,which demonstrates the effectiveness of the developed algorithms and methods.展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A...In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.展开更多
In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to for...In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.展开更多
Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop ...Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.展开更多
This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequal...This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.展开更多
Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations i...Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.展开更多
A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and ...A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribu- tion correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds num- ber is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.展开更多
Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the ...Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to展开更多
Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of...Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.展开更多
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and gene...First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.展开更多
Solving nonlinear evolution partial differential equations has been a longstanding computational challenge.In this paper,we present a universal paradigm of learning the system and extracting patterns from data generat...Solving nonlinear evolution partial differential equations has been a longstanding computational challenge.In this paper,we present a universal paradigm of learning the system and extracting patterns from data generated from experiments.Specifically,this framework approximates the latent solution with a deep neural network,which is trained with the constraint of underlying physical laws usually expressed by some equations.In particular,we test the effectiveness of the approach for the Burgers'equation used as an example of second-order nonlinear evolution equations under different initial and boundary conditions.The results also indicate that for soliton solutions,the model training costs significantly less time than other initial conditions.展开更多
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
文摘By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.
基金Supported by National Natural Science Foundation of China (10671069)
文摘Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.
文摘Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.
基金partially supported by the NSF of China(12271226)partially supported by the NSF of China(12201434)+4 种基金the NSF of Gansu Province of China(21JR7RA537)the NSF of Gansu Province of China(21JR7RA535)the Fundamental Research Funds for the Central Universities(lzujbky-2021-kb15)partially supported by the NSF of China(12371170)the R&D Program of Beijing Municipal Education Commission(KM202310028017)。
文摘It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied,and the known results on the interface dynamics of this equation are under the compactly supported initial value.Moreover,there was no explicit formula regarding the interface due to the peculiarity of nonlocal dispersal operators.Anatural question is whether it is possible to provide a precise characterization of the interface with respect to small parameter for the general initial values(including exponentially bounded and unbounded).This paper is concerned with the interface dynamics of the nonlocal dispersal equation with scaling parameter.For the exponentially bounded initial value,by choosing the hyperbolic scaling,we show that at a very small time,the interface is confined within a generated layer whose thickness is at most O(√ɛ|ln ɛ|),,and subsequently,the interface propagates at a linear speed determined by the decay rate of initial value.For a class of exponentially unbounded initial value,by introducing the nonlinear scaling based on the decay of initial value,we deduce the corresponding Hamilton-Jacobi equation and describe precisely the propagation of the interface,which provides a superlinear speed of the interface.The investigation of the interface dynamics under different scaling reflects multiplex propagation modes in spatial dynamics and provides a new perspective on the wave propagation in nonlocal dispersal equations.
基金supported in part by NSFC(Grant Nos.12271205,12171498).
文摘In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniqueness results for steady symmetric transonic shock solutions to the nonisentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a symmetric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.
基金supported by the Key Project of the NSFC(12131010)the NSFC(12271032)+2 种基金supported by the NSFC(12371205)the NSF of Guangdong Province(2025A1515012026)supported by the NSF of Guangdong Province(2024A1515013238)。
文摘In this paper,we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel,which can describe the interaction between a binary material and the walls of the physical domain.We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.
基金carried out within the framework of the state assignment of KIAM RAS(No.125020701776-0).
文摘The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These methods allow to effectively suppress oscillations,including in velocity profiles,as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations.The methods can be applied both in explicit and implicit(method of separate sweeps)iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer,as well as in solving problems of magnetohydrodynamics and computational astrophysics.In order to avoid loss of solution accuracy on spatially non-uniform grids,in this work an algorithm of grid embeddings is developed,which is applied near transition points between cells of different sizes.The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes.Calculations are performed for the classical problem of decay of an arbitrary discontinuity(Sod’s problem)and the problem of propagation of two symmetric rarefaction waves in opposite directions(Einfeldt’s problem).In the case of using different methods for selecting the AAV,a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed.As a result of the comparative analysis,the applicability of these methods is shown in the spatially one-dimensional case(explicit and implicit iterative processes).The obtained results are compared with the data from the literature.The results coincide with analytical solutions with high accuracy,where the relative error does not exceed 0.1%,which demonstrates the effectiveness of the developed algorithms and methods.
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11562014,11762011,11671101,71471020,51839002the Natural Science Foundation of Inner Mongolia under Grant No.2017MS0108+4 种基金Hunan Provincial Natural Science Foundation of China under Grant No.2016JJ2061the Scientific Research Fund of Hunan Provincial Education Department under Grant No.18A325the Construct Program of the Key Discipline in Hunan Province under Grant No.201176the Aid Program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province under Grant No.2014207Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology under Grant No.018MMAEZD191
文摘In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.
基金co-supported by the National Natural Science Foundation of China (Nos. 61333011, 91216304 and 61121003)
文摘In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.
文摘Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.
基金Supported by the NNSF of China(11071222)Supported by the NSF of Hunan Province(12JJ6006)Supported by Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)
文摘This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.
文摘Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China(No.11132008)
文摘A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribu- tion correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds num- ber is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.
文摘Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014)the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province,China (Grant No. CXLX12_0720)
文摘Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
文摘First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.
基金supported by the National Natural Science Foundation of China(No.11675054)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)Science and Technology Commission of Shanghai Municipality(No.18dz2271000)。
文摘Solving nonlinear evolution partial differential equations has been a longstanding computational challenge.In this paper,we present a universal paradigm of learning the system and extracting patterns from data generated from experiments.Specifically,this framework approximates the latent solution with a deep neural network,which is trained with the constraint of underlying physical laws usually expressed by some equations.In particular,we test the effectiveness of the approach for the Burgers'equation used as an example of second-order nonlinear evolution equations under different initial and boundary conditions.The results also indicate that for soliton solutions,the model training costs significantly less time than other initial conditions.
