By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler Lagrange equations...By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler Lagrange equations and Hamilton＇s canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.展开更多
-Starting from physical oceanology characteristics of the China seas and for the short-term operational prediction of SST in the region, a two-dimensional (vertically integrated) primitive equation model, physically r...-Starting from physical oceanology characteristics of the China seas and for the short-term operational prediction of SST in the region, a two-dimensional (vertically integrated) primitive equation model, physically reasonable and operationally feasible,on the upper mixed layer is constructed and given here, which consists of three parts, the nondivergent residual current (the monthly mean field of the Kuroshio and its branches) equations, the dynamic forecasting equations, and the equation of model's physics consisting of surface heat flux, coolings of the upper mixed layer due to the Ekman pumping and the entrainment by gale. This model may be used primarily to forecast the sea surface temperature, and to give estimations of the mean wind-driven current and the sea level, for a period of 3-5 d. In part 1 of this series, the physical conditions for establishing model equations are discussed first, that is, 1. the existence of the upper well mixed layer in the region; 2. the distinguishability of currents of all kinds; 3. the splitting of thermodynamical equation. The equations of nondivergent residual current, and the dynamic forecasting equations with initial values and boundary conditions are also discussed.展开更多
In the present paper, some additional new definitions on the kinematics and dynamics are introduced, and the dynamical equations of Boussinesq type, Kirchhoff type, Signorini type and Nowozilov type for finite deforma...In the present paper, some additional new definitions on the kinematics and dynamics are introduced, and the dynamical equations of Boussinesq type, Kirchhoff type, Signorini type and Nowozilov type for finite deformable polar elastic media are systematically derived from the consideration of Euler angles as angular coordinates and the dynamical equations of Cauchy type presented by Dluzewski.展开更多
This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber wh...This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber where the stimulated Raman scattering effect is bethinking during modeling. The ultimate goal of this work is to propose a plateful of solutions likely to serve as signals during studies on computer or laboratory propagation studies. The resolution of such an equation is not always the easiest thing, and we used the Bogning-Djeumen Tchaho-Kofané method extended to the implicit functions of Bogning to obtain the results. The flexibility of the iB-functions made it possible to deduce the trigonometric solutions, from the obtained solitary wave solutions with a hyperbolic analytical sequence of the studied Sasa-Satsuma equation. A better appreciation of the nature of the solutions obtained is made through the profiles of some solutions obtained during the different analyses.展开更多
In this paper the concrete forms o f dyn amical equations for finite deformable polar elastic media of Boussinesq type, K irchhoff type, Signorini type and Novozhilov type with the help of the anholono mic physical f...In this paper the concrete forms o f dyn amical equations for finite deformable polar elastic media of Boussinesq type, K irchhoff type, Signorini type and Novozhilov type with the help of the anholono mic physical frame method are derived.展开更多
This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian ...This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.展开更多
In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three p...In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens. The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations. The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.展开更多
A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only res...A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.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
A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate ...A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.展开更多
： 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
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
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
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
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T w...This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.展开更多
In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,w...In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,where n≥2,φ(u)=|u|^(γ)sgn(u)forγ>0,ri(1≤i≤n)are positive rd-continuous functions and h∈C_(rd)(T,(0,∞)).The functionτ∈C_(rd)(T,T)satisfiesτ(t)≤t and lim_(t→∞)τ(t)=∞and f∈C(R,R).By using a generalized Riccati transformation,we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.The obtained results are new for the corresponding higher order differential equations and difference equations.In the end,some applications and examples are provided to illustrate the importance of the main results.展开更多
The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the flui...The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact in- terface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This pa- per describes the field affected by the gravity constraints. Applying the multi-scale anal- ysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analy- sis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic per- turbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.展开更多
This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corres...This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka(Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. Demonstratio Math., 2018, 51: 198–210).展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 19572018）.
文摘By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler Lagrange equations and Hamilton＇s canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.
文摘-Starting from physical oceanology characteristics of the China seas and for the short-term operational prediction of SST in the region, a two-dimensional (vertically integrated) primitive equation model, physically reasonable and operationally feasible,on the upper mixed layer is constructed and given here, which consists of three parts, the nondivergent residual current (the monthly mean field of the Kuroshio and its branches) equations, the dynamic forecasting equations, and the equation of model's physics consisting of surface heat flux, coolings of the upper mixed layer due to the Ekman pumping and the entrainment by gale. This model may be used primarily to forecast the sea surface temperature, and to give estimations of the mean wind-driven current and the sea level, for a period of 3-5 d. In part 1 of this series, the physical conditions for establishing model equations are discussed first, that is, 1. the existence of the upper well mixed layer in the region; 2. the distinguishability of currents of all kinds; 3. the splitting of thermodynamical equation. The equations of nondivergent residual current, and the dynamic forecasting equations with initial values and boundary conditions are also discussed.
文摘In the present paper, some additional new definitions on the kinematics and dynamics are introduced, and the dynamical equations of Boussinesq type, Kirchhoff type, Signorini type and Nowozilov type for finite deformable polar elastic media are systematically derived from the consideration of Euler angles as angular coordinates and the dynamical equations of Cauchy type presented by Dluzewski.
文摘This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber where the stimulated Raman scattering effect is bethinking during modeling. The ultimate goal of this work is to propose a plateful of solutions likely to serve as signals during studies on computer or laboratory propagation studies. The resolution of such an equation is not always the easiest thing, and we used the Bogning-Djeumen Tchaho-Kofané method extended to the implicit functions of Bogning to obtain the results. The flexibility of the iB-functions made it possible to deduce the trigonometric solutions, from the obtained solitary wave solutions with a hyperbolic analytical sequence of the studied Sasa-Satsuma equation. A better appreciation of the nature of the solutions obtained is made through the profiles of some solutions obtained during the different analyses.
文摘In this paper the concrete forms o f dyn amical equations for finite deformable polar elastic media of Boussinesq type, K irchhoff type, Signorini type and Novozhilov type with the help of the anholono mic physical frame method are derived.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10675088)
文摘This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.
文摘In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens. The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations. The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.
文摘A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.
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A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.
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.
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.
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Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
基金supported in part by the NNSF of China(10971231 and 11271379)
文摘This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.
基金supported by the Jiangxi Provincial Natural Science Foundation(20202BABL211003)the Science and Technology Project of Jiangxi Education Department(GJJ180354).
文摘In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,where n≥2,φ(u)=|u|^(γ)sgn(u)forγ>0,ri(1≤i≤n)are positive rd-continuous functions and h∈C_(rd)(T,(0,∞)).The functionτ∈C_(rd)(T,T)satisfiesτ(t)≤t and lim_(t→∞)τ(t)=∞and f∈C(R,R).By using a generalized Riccati transformation,we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.The obtained results are new for the corresponding higher order differential equations and difference equations.In the end,some applications and examples are provided to illustrate the importance of the main results.
基金Project supported by the National Natural Science Foundation of China (No. 10871225)the Pujiang Talent Program of China (No. 06PJ14416)
文摘The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact in- terface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This pa- per describes the field affected by the gravity constraints. Applying the multi-scale anal- ysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analy- sis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic per- turbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.
文摘In this paper, the dynamic equations for Koiter shells have been studied by Galerkin method, the existence and uniqueness to the solutions are proved.
文摘This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka(Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. Demonstratio Math., 2018, 51: 198–210).
