We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system...We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.展开更多
With the development of IT,more andmore document resources are available over the Internet.Inorder to facilitate users’retrieval of the digital documents,Integrations of the multi source systems are necessary,Sinceth...With the development of IT,more andmore document resources are available over the Internet.Inorder to facilitate users’retrieval of the digital documents,Integrations of the multi source systems are necessary,Sincethe individual sources collect their information independently,the same papers may be stored in different source systems.The traditional solutions to the redundancy problems in thedistributed environments are usually based on the globalcatalogs which keep the redundancy information for thesyst...展开更多
This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less impor...This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time,before the damping forces can dissipate a significant portion of the energy input into the system.The development of two sine series solutions,relating to different types of impulsive loadings,one involving a single concentrated force and the other a distributed line load,are presented.This study revealed that when a simply supported Euler-Bernoulli beam,resting on a Winkler soil model,is subject to an impact load,the resulting vertical displacements,bending moments and shear forces produced along the span of the beam are considerably affected.In particular,the quantification of this effect is best observed,relative to the corresponding static solution,via an amplification factor.The computed impact amplification factors,for the sub-grade moduli used in this study,were in magnitude greater than 2,thus confirming the multiple-degree-of-freedom nature of the problem.展开更多
All-inorganic cesium lead halide perovskites （CsPbX3, X=CF, Br-, I-） could provide comparableoptoelectronic properties as a promising class of materials for photovoltaic cell （PV）, photodetector andlight-emitting ...All-inorganic cesium lead halide perovskites （CsPbX3, X=CF, Br-, I-） could provide comparableoptoelectronic properties as a promising class of materials for photovoltaic cell （PV）, photodetector andlight-emitting diode （LED） with enhanced thermal and moisture stabilities compared to organic-inorganic lead halide species. However, fabrication of CsPbI3 perovskite via facile solution process hasbeen difficult due to instability of CsPbl3 in the perovskite cubic phase in ambient air. Herein, we reportthe synthesis of CsPbl3 perovskite microcrystals by low-temperature, catalyst-free, solution-phasemethod. By applying the time-resolve spectroscopic technique, we determine the carrier diffusioncoefficient of 0.6-1.2 cm2/s, the intrinsic carrier lifetimes of 200-1300 ns and diffusion length of4-10 μm in different individual CsPbl3 perovskite microcrystals. Our results suggest the CsPbl3 perovskitemicrocrystals synthesized by solution process exhibit high quality feature and are suitable forapplications in optoelectronic devices.展开更多
This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensiona...This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.展开更多
How to determine accurately the association states of solutes in aqueous systems is of fundamental importance in a variety of chemical, physical, and biological processes, We apply four widely used criteria to analyze...How to determine accurately the association states of solutes in aqueous systems is of fundamental importance in a variety of chemical, physical, and biological processes, We apply four widely used criteria to analyze the dynamic association processes of solutes, e.g., amphiphilic molecules, and to find the inappropriate selections of representative sites on solutes in these criteria may bring about appreciable influence on the estimation of dynamic association behaviors such as unrealistic packing radii and even misleading packing structures. It would be better to select dynamically representative sites on solute molecules based on the characteristic of solute associations. Our detailed discussions give a guide on how to determine an appropriate criterion to accurately analyze the association behaviors of solute molecules in aqueous solutions.展开更多
The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rat...The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rates of ponicidin are computed with this model from ~C relaxation parameters.展开更多
Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variabl...Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.展开更多
This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are s...This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are satisfied展开更多
All-atom molecular dynamics （MD） simulations and chemical shifts were used to study interactions and structures in the glycine-water system. Radial distribution functions and the hydrogen-bond network were applied i...All-atom molecular dynamics （MD） simulations and chemical shifts were used to study interactions and structures in the glycine-water system. Radial distribution functions and the hydrogen-bond network were applied in MD simulations. Aggregates in the aqueous glycine solution could be classified into different regions by analysis of the hydrogen-bonding network. Temperature-dependent NMR spectra and the viscosity of glycine in aqueous solutions were measured to compare with the results of MD simulations. The variation tendencies of the hydrogen atom chemical shifts and viscosity with concentration of glycine agree with the statistical results of hydrogen bonds in the MD simulations.展开更多
Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J...Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.展开更多
The diffusion coefficients(Dapp) and the heterogeneous electron transfer rate constants(ks)for ferrocene in several polymer solvents were determined by using steady-stae voltammetry. Thetemperature dependence of the t...The diffusion coefficients(Dapp) and the heterogeneous electron transfer rate constants(ks)for ferrocene in several polymer solvents were determined by using steady-stae voltammetry. Thetemperature dependence of the two parameters indicates Arrhenius behavior. The polymer solventeffects on diffusion and electron transfer dynamics of ferrocene were discussed展开更多
Mono-alkyl-functionalized pillar[5]arenes PI, P2, and P3 were synthesized by click reaction, which exhibited different self-assembly behavior in polar solvent DMSO. Stable pseudo[ 1 ]rotaxane was formed by the self-co...Mono-alkyl-functionalized pillar[5]arenes PI, P2, and P3 were synthesized by click reaction, which exhibited different self-assembly behavior in polar solvent DMSO. Stable pseudo[ 1 ]rotaxane was formed by the self-complexation from P1 or P2, whereas, concentration-dependent pseudorotaxane structures were generated by P3 which bearing more flexible side chain. Interestingly, the obtained pseudo[1]rotaxanes exhibited a dynamic fast assembly process upon adding NaBF4, resulting in the formation of Na＋-induced pseudorotaxanes.展开更多
In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(...In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(G’/G,1/G)-expansion method.Computer software,like Mathematica,is used to complete this discussion.The obtained solutions of the proposed equation are classified into trigonometric,hyperbolic,and rational types which play an important role in searching for numerous scientific events.The technique employed here is an extension of the(G’/G)-expansion technique for finding all previously discovered solutions.To illustrate our findings more clearly,we provide 2D and 3D charts of the various recovery methods.We then contrasted our findings with those of past solutions.The graphical illustrations of the acquired solutions are singular periodic solitons and kink solitons which are added at the end of this paper.展开更多
The diffusion coefficients(Dapp) and the heterogeneous electron-transfer rate constants(ks)for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steadystate voltammetry. The two p...The diffusion coefficients(Dapp) and the heterogeneous electron-transfer rate constants(ks)for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steadystate voltammetry. The two parameters increase with increasing temperature, indicating Arrhenius behavior. The effects of the nature of electroactive solute molecules on Dapp, ks, and the half-wave potentials(E1/2) are discussed.展开更多
The ditheion coefficients(Dapp) and the heterogeneous electron-transfer rate constan(ks)for ferrocene in MPEG/salt electrolytes were determined by using Steady-stae voltammetry. The temperature dependence of the two p...The ditheion coefficients(Dapp) and the heterogeneous electron-transfer rate constan(ks)for ferrocene in MPEG/salt electrolytes were determined by using Steady-stae voltammetry. The temperature dependence of the two parameters obeys the Arrhenius equstion. The effect of the ionic size of sir supporting electrolytes on diffusion and electron transfer dynamics of fermcene was discussed展开更多
It is demonstrated that when tension leg platform （TLP） moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP,...It is demonstrated that when tension leg platform （TLP） moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP, The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theo- retical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displace- ment, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force, Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.展开更多
We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particu...We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particular, the double peakon solutions of both equations are investigated in detail. At the same time, the dynamic behaviors of three types double peakon solutions are analyzed by some figures.展开更多
This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink s...This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.展开更多
Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the ta...Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.展开更多
文摘We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.
文摘With the development of IT,more andmore document resources are available over the Internet.Inorder to facilitate users’retrieval of the digital documents,Integrations of the multi source systems are necessary,Sincethe individual sources collect their information independently,the same papers may be stored in different source systems.The traditional solutions to the redundancy problems in thedistributed environments are usually based on the globalcatalogs which keep the redundancy information for thesyst...
基金l’UniversitéLaval for the financial support of his sabbatical year at Dipartimento di Bioscienze e Territorio,Universitàdegli Studi del Molise in Campobasso,Italy。
文摘This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time,before the damping forces can dissipate a significant portion of the energy input into the system.The development of two sine series solutions,relating to different types of impulsive loadings,one involving a single concentrated force and the other a distributed line load,are presented.This study revealed that when a simply supported Euler-Bernoulli beam,resting on a Winkler soil model,is subject to an impact load,the resulting vertical displacements,bending moments and shear forces produced along the span of the beam are considerably affected.In particular,the quantification of this effect is best observed,relative to the corresponding static solution,via an amplification factor.The computed impact amplification factors,for the sub-grade moduli used in this study,were in magnitude greater than 2,thus confirming the multiple-degree-of-freedom nature of the problem.
基金the financial support from the National Natural Science Foundation of China(No.21473192)the financial support from the National Natural Science Foundation of China(Nos.21373042 and 21677029)
文摘All-inorganic cesium lead halide perovskites （CsPbX3, X=CF, Br-, I-） could provide comparableoptoelectronic properties as a promising class of materials for photovoltaic cell （PV）, photodetector andlight-emitting diode （LED） with enhanced thermal and moisture stabilities compared to organic-inorganic lead halide species. However, fabrication of CsPbI3 perovskite via facile solution process hasbeen difficult due to instability of CsPbl3 in the perovskite cubic phase in ambient air. Herein, we reportthe synthesis of CsPbl3 perovskite microcrystals by low-temperature, catalyst-free, solution-phasemethod. By applying the time-resolve spectroscopic technique, we determine the carrier diffusioncoefficient of 0.6-1.2 cm2/s, the intrinsic carrier lifetimes of 200-1300 ns and diffusion length of4-10 μm in different individual CsPbl3 perovskite microcrystals. Our results suggest the CsPbl3 perovskitemicrocrystals synthesized by solution process exhibit high quality feature and are suitable forapplications in optoelectronic devices.
文摘This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.
基金Supported by the National Science Fund for Outstanding Young Scholars under Grant No 11422542the Key Research Program of Chinese Academy of Sciences under Grant No KJZD-EW-M03,KIPCAS+1 种基金the Shanghai Supercomputer Center of Chinathe High Performance Computing Center of Shanghai University
文摘How to determine accurately the association states of solutes in aqueous systems is of fundamental importance in a variety of chemical, physical, and biological processes, We apply four widely used criteria to analyze the dynamic association processes of solutes, e.g., amphiphilic molecules, and to find the inappropriate selections of representative sites on solutes in these criteria may bring about appreciable influence on the estimation of dynamic association behaviors such as unrealistic packing radii and even misleading packing structures. It would be better to select dynamically representative sites on solute molecules based on the characteristic of solute associations. Our detailed discussions give a guide on how to determine an appropriate criterion to accurately analyze the association behaviors of solute molecules in aqueous solutions.
文摘The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rates of ponicidin are computed with this model from ~C relaxation parameters.
文摘Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.
文摘This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are satisfied
基金Supported by the National Natural Science Foundation of China(No.20903026)the Talents Introduction Foundation for Universities of Guangdong Province(2011)Scientific Research Foundation of the Natural Science Foundation of Guangdong Province(No.S2011010002483)
文摘All-atom molecular dynamics （MD） simulations and chemical shifts were used to study interactions and structures in the glycine-water system. Radial distribution functions and the hydrogen-bond network were applied in MD simulations. Aggregates in the aqueous glycine solution could be classified into different regions by analysis of the hydrogen-bonding network. Temperature-dependent NMR spectra and the viscosity of glycine in aqueous solutions were measured to compare with the results of MD simulations. The variation tendencies of the hydrogen atom chemical shifts and viscosity with concentration of glycine agree with the statistical results of hydrogen bonds in the MD simulations.
文摘Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.
文摘The diffusion coefficients(Dapp) and the heterogeneous electron transfer rate constants(ks)for ferrocene in several polymer solvents were determined by using steady-stae voltammetry. Thetemperature dependence of the two parameters indicates Arrhenius behavior. The polymer solventeffects on diffusion and electron transfer dynamics of ferrocene were discussed
基金the financial support from the National Natural Science Foundation of China(Nos.21472089,21572101)the National Natural Science Foundation of Jiangsu(No.BK20140595)
文摘Mono-alkyl-functionalized pillar[5]arenes PI, P2, and P3 were synthesized by click reaction, which exhibited different self-assembly behavior in polar solvent DMSO. Stable pseudo[ 1 ]rotaxane was formed by the self-complexation from P1 or P2, whereas, concentration-dependent pseudorotaxane structures were generated by P3 which bearing more flexible side chain. Interestingly, the obtained pseudo[1]rotaxanes exhibited a dynamic fast assembly process upon adding NaBF4, resulting in the formation of Na＋-induced pseudorotaxanes.
文摘In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(G’/G,1/G)-expansion method.Computer software,like Mathematica,is used to complete this discussion.The obtained solutions of the proposed equation are classified into trigonometric,hyperbolic,and rational types which play an important role in searching for numerous scientific events.The technique employed here is an extension of the(G’/G)-expansion technique for finding all previously discovered solutions.To illustrate our findings more clearly,we provide 2D and 3D charts of the various recovery methods.We then contrasted our findings with those of past solutions.The graphical illustrations of the acquired solutions are singular periodic solitons and kink solitons which are added at the end of this paper.
文摘The diffusion coefficients(Dapp) and the heterogeneous electron-transfer rate constants(ks)for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steadystate voltammetry. The two parameters increase with increasing temperature, indicating Arrhenius behavior. The effects of the nature of electroactive solute molecules on Dapp, ks, and the half-wave potentials(E1/2) are discussed.
文摘The ditheion coefficients(Dapp) and the heterogeneous electron-transfer rate constan(ks)for ferrocene in MPEG/salt electrolytes were determined by using Steady-stae voltammetry. The temperature dependence of the two parameters obeys the Arrhenius equstion. The effect of the ionic size of sir supporting electrolytes on diffusion and electron transfer dynamics of fermcene was discussed
基金Project supported by "Creativeness Project of the Tenth Five-Year Plan" of Chinese Academy of Sciences (No.KJCX2-SW-L03)the National High-Tech Research and Development Program of China (863 Program) (No.2004AA617010)
文摘It is demonstrated that when tension leg platform （TLP） moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP, The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theo- retical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displace- ment, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force, Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particular, the double peakon solutions of both equations are investigated in detail. At the same time, the dynamic behaviors of three types double peakon solutions are analyzed by some figures.
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.
文摘Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.
