We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an elect...We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered lattices.Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene systems.Unlike the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.展开更多
An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to captur...An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections:the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.展开更多
Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model....Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model. Three types of period-one states were found, with different periods of injection time delay τ_(inj), 2τ_(inj), and reciprocal of the detuning frequency. Besides, square-wave, quasi-period, pulse-burst and chaotic oscillations were also observed. It is concluded that external-cavity periodic dynamics and optical modes beating are the mainly periodic dynamics. The interaction of the two periodic dynamics and the high-frequency dynamics stimulated by strong injection induces the dynamic states evolution.This work helps to understand the dynamic behaviors in QCLs and shows a new way to mid-infrared wide-band chaotic laser.展开更多
We theoretically study periodic oscillation and its period of a circadian rhythm model of Neurospora and provide the conditions for the existence of such a periodic oscillation by the theory of competitive dynamical s...We theoretically study periodic oscillation and its period of a circadian rhythm model of Neurospora and provide the conditions for the existence of such a periodic oscillation by the theory of competitive dynamical systems.To present the exact expression of the unique equilibrium in terms of parameters of system,we divide them into eleven classes for the Hill coefficient n=1 or n=2,among seven classes of which nontrivial periodic oscillations exist.Numerical simulations are made among the seven classes and the models with the Hill coefficient n=3 or n=4 to reveal the influence of parameter variation on periodic oscillations and their periods.The results show that their periods of the periodic oscillations are approximately 21.5 h,which coincides with the known experiment result observed in constant darkness.展开更多
Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynam...Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.展开更多
In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic...In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth (e 〉 0) and discontin- uous (ce = 0) stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems.展开更多
Sufficient conditions are obtained for the existence, uniqueness and stability of T-periodic solutions far the Hopfield neural network equations with delay [GRAPHICS]
We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during t...We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.展开更多
It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study ...It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.展开更多
In this paper,the dynamic behaviors of the cavitation bubble near a fixed spherical particle during the second oscillation period are analyzed based on the high-speed photographic system.The deformation and motion of ...In this paper,the dynamic behaviors of the cavitation bubble near a fixed spherical particle during the second oscillation period are analyzed based on the high-speed photographic system.The deformation and motion of the bubble during the second period are investigated by changing the distance between the particle and the bubble and the maximum radius of the bubble.Meanwhile,the variation of the equivalent radius and the centroid motions are analyzed,and the dynamic behaviors of the bubble are categorized according to the bubble morphological characteristics during the second period.Through this research,it is found that(1)The dynamic behaviors of the bubble during the second oscillation period could be divided into three typical cases:For case 1,a bulge would exist on the bubble interface away from the particle,and for case 2,a bulge would appear on the bubble interface and evolve towards the particle,while for case 3,the bubble would be divided into two parts.(2)The larger the dimensionless distance between the particle and the bubble,the smaller the maximum bubble equivalent radius in the second period,and the shorter the second oscillation period.(3)When the bubble is close to the particle,a counter-jet appears at the bubble interface away from the particle during the rebound stage.展开更多
Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography are investigated by numerical simulations based on a Mixed Euler–Lagrange(MEL) method. The transition is accomplis...Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography are investigated by numerical simulations based on a Mixed Euler–Lagrange(MEL) method. The transition is accomplished by the ship traveling from the depth h1 into the depth h2 via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms under free-surface condition to prevent waves in the upstream. Evidently, it cannot be applied to the present problem due to upstream waves generated by the ship would be dampened by the upwind scheme. The central differential scheme provides more accurate results,but it is not unconditionally stable. An MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships.The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.展开更多
The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible is...The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained. And the first integral of the equation was then carded out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed, and the corresponding numerical examples were carded out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely. That is to say, the shell will be destroyed ultimately.展开更多
Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relativ...Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device (CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.展开更多
The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathemati...The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.展开更多
The photoinduced bulk polymerization of a reactive-hindered amine light stabilizers (r-HALS), 4-acryloyl-2, 2, 6,6-tetramethylpiperidinyl (ATMP), was performed at 80 C by using a DPC technique. An unique periodic expo...The photoinduced bulk polymerization of a reactive-hindered amine light stabilizers (r-HALS), 4-acryloyl-2, 2, 6,6-tetramethylpiperidinyl (ATMP), was performed at 80 C by using a DPC technique. An unique periodic exponential attenuation-type oscillating curve was found when the polymerization was carried out in air, but this phenomenon was not found in nitrogen. It is supposed that this unique kinetic performance may be attributed to nitroxyl radicals that are produced in situ from the oxidation of ATMP. ATMP polymer with narrow polydispersity (d = 1.03) can be obtained by photoinduced solution polymerization of ATMP. The signal detected in ESR may be assigned to the nitroxyl radicals in the matrix of ATMP polymer. Since this kind of recycling of nitroxyl radicals is well documented for the photostabilizing mechanism of HALS, the present results may serve as a kinetic evidence for this mechanism.展开更多
Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i) The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii)...Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i) The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.展开更多
Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a sta...Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.展开更多
We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determine...We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper(AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of underdamped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength.Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.展开更多
Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic...Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic step loads at its inner and outer surfaces. A second-order nonlinear ordinary differential equation approximately describing radially symmetric motion of the membrane is obtained by setting the thick- ness of the spherical structure close to one. The qualitative properties of the solutions are discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane are proposed. In certain cases, it is proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type "∞", and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11874316)the National Basic Research Program of China(Grant No.2015CB921103)the International Visiting Faculty Program of Hunan Provincial Government,China.
文摘We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered lattices.Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene systems.Unlike the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.
基金supported by the National Natural Science Foundation of China (10872096)the Open Fund of State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology (KFJJ09-13)
文摘An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections:the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.
基金Project supported by the National Key Research and Development Program of China (Grant No. 2019YFB1803500)the National Natural Science Foundation of China (Grant No. 61805168)+4 种基金the Natural Science Foundation of Shanxi Province, China (Grant Nos. 201801D221183 and 20210302123185)International Cooperation of Key Research and Development Program of Shanxi Province (Grant No. 201903D421012)Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2021-032)Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2019L0133)Fund for Shanxi “1331 Project” Key Innovative Research Team。
文摘Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model. Three types of period-one states were found, with different periods of injection time delay τ_(inj), 2τ_(inj), and reciprocal of the detuning frequency. Besides, square-wave, quasi-period, pulse-burst and chaotic oscillations were also observed. It is concluded that external-cavity periodic dynamics and optical modes beating are the mainly periodic dynamics. The interaction of the two periodic dynamics and the high-frequency dynamics stimulated by strong injection induces the dynamic states evolution.This work helps to understand the dynamic behaviors in QCLs and shows a new way to mid-infrared wide-band chaotic laser.
基金This work was supported by the National Natural Science Foundation of China(NSFC)(No.11771295).
文摘We theoretically study periodic oscillation and its period of a circadian rhythm model of Neurospora and provide the conditions for the existence of such a periodic oscillation by the theory of competitive dynamical systems.To present the exact expression of the unique equilibrium in terms of parameters of system,we divide them into eleven classes for the Hill coefficient n=1 or n=2,among seven classes of which nontrivial periodic oscillations exist.Numerical simulations are made among the seven classes and the models with the Hill coefficient n=3 or n=4 to reveal the influence of parameter variation on periodic oscillations and their periods.The results show that their periods of the periodic oscillations are approximately 21.5 h,which coincides with the known experiment result observed in constant darkness.
基金the National Natural Science Foundation of China(Nos.10772104 and10402018)the Shanghai Leading Academic Discipline Project(No.Y0103)
文摘Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.
基金supported by the National Natural Science Foundation of China(11072065)
文摘In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth (e 〉 0) and discontin- uous (ce = 0) stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems.
文摘Sufficient conditions are obtained for the existence, uniqueness and stability of T-periodic solutions far the Hopfield neural network equations with delay [GRAPHICS]
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12022513, 11775176, 11947301, and 12047502)the Major Basic Research Program of the Natural Science of Foundation of Shaanxi Province, China (Grant Nos. 2018KJXX-094 and 2017KCT-12)。
文摘We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11272209)the State Key Laboratory of Ocean Engineering(Grant No.GKZD010059)
文摘It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51976056,52076215).
文摘In this paper,the dynamic behaviors of the cavitation bubble near a fixed spherical particle during the second oscillation period are analyzed based on the high-speed photographic system.The deformation and motion of the bubble during the second period are investigated by changing the distance between the particle and the bubble and the maximum radius of the bubble.Meanwhile,the variation of the equivalent radius and the centroid motions are analyzed,and the dynamic behaviors of the bubble are categorized according to the bubble morphological characteristics during the second period.Through this research,it is found that(1)The dynamic behaviors of the bubble during the second oscillation period could be divided into three typical cases:For case 1,a bulge would exist on the bubble interface away from the particle,and for case 2,a bulge would appear on the bubble interface and evolve towards the particle,while for case 3,the bubble would be divided into two parts.(2)The larger the dimensionless distance between the particle and the bubble,the smaller the maximum bubble equivalent radius in the second period,and the shorter the second oscillation period.(3)When the bubble is close to the particle,a counter-jet appears at the bubble interface away from the particle during the rebound stage.
基金financially supported by Natural Scienceof University of Jiangsu Province (Grant No.22KJB580004)the Key R&D Projects in Guangdong Province (Grant No.2020B1111500001)the Jiangsu Province“Six Talents Peak”High-Level Talents Support Project (Grant No.2018-KTHY-033)。
文摘Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography are investigated by numerical simulations based on a Mixed Euler–Lagrange(MEL) method. The transition is accomplished by the ship traveling from the depth h1 into the depth h2 via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms under free-surface condition to prevent waves in the upstream. Evidently, it cannot be applied to the present problem due to upstream waves generated by the ship would be dampened by the upwind scheme. The central differential scheme provides more accurate results,but it is not unconditionally stable. An MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships.The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.
基金国家自然科学基金,Municipal Key Subject Program of Shanghai
文摘The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained. And the first integral of the equation was then carded out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed, and the corresponding numerical examples were carded out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely. That is to say, the shell will be destroyed ultimately.
基金financially supported by the National Natural Science Foundation of China(Grant No.11272079)the National Basic Research Program of China(973 Program,Grant No.2011CB013702)
文摘Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device (CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.
基金supported by the National Natural Science Foundation of China (Nos. 10872045 and10721062)the Program for New Century Excellent Talents in University (No. NCET-09-0096)the Fundamental Research Funds for the Central Universities (No. DC10030104)
文摘The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.
基金the National Natural Science Foundation of China(No.20274023)key project foundation of National Ministry of Education(No.02114)Guangdong Province Natural Science Foundation of China(No.021241)for supporting this work.
文摘The photoinduced bulk polymerization of a reactive-hindered amine light stabilizers (r-HALS), 4-acryloyl-2, 2, 6,6-tetramethylpiperidinyl (ATMP), was performed at 80 C by using a DPC technique. An unique periodic exponential attenuation-type oscillating curve was found when the polymerization was carried out in air, but this phenomenon was not found in nitrogen. It is supposed that this unique kinetic performance may be attributed to nitroxyl radicals that are produced in situ from the oxidation of ATMP. ATMP polymer with narrow polydispersity (d = 1.03) can be obtained by photoinduced solution polymerization of ATMP. The signal detected in ESR may be assigned to the nitroxyl radicals in the matrix of ATMP polymer. Since this kind of recycling of nitroxyl radicals is well documented for the photostabilizing mechanism of HALS, the present results may serve as a kinetic evidence for this mechanism.
文摘Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i) The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.
文摘Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.
基金supported by the National Natural Science Foundation of China(Grant Nos.11874316,and 11474244)the National Basic Research Program of China(Grant No.2015CB921103)+1 种基金the Innovative Research Team in University(Grant No.IRT 17R91)the International Visiting Faculty Program of Hunan Provincial Government,China。
文摘We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper(AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of underdamped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength.Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.
基金supported by the National Natural Science Foundation of China (Nos.10872045, 10721062,and 10772104)the Program for New Century Excellent Talents in University (No.NCET-09-0096)+1 种基金the Post-Doctoral Science Foundation of China (No.20070421049)the Fundamental Research Funds for the Central Universities (No.DC10030104)
文摘Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic step loads at its inner and outer surfaces. A second-order nonlinear ordinary differential equation approximately describing radially symmetric motion of the membrane is obtained by setting the thick- ness of the spherical structure close to one. The qualitative properties of the solutions are discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane are proposed. In certain cases, it is proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type "∞", and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.