Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the p...Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the previous work.The present paper aims to explore composite fast-slow dynamics when the frequency ratio is variable.As a result,a novel route to composite fast-slow dynamics is obtained.We find that,when presented with variable frequency ratios in a 1:n fashion,the sliding fast-slow oscillations may turn into the ones characterized by the fact that the clusters of large-amplitude oscillations of relaxational type are exhibited in each period of the oscillations,and hence the mixedmode fast-slow oscillations.Depending on whether the transition of the trajectory is from the upper subsystem via the fold bifurcation or not,these interesting oscillations are divided into two classes,both of which are investigated numerically.Our study shows that,when the frequency ratio n is increased from n=3,newly created boundary equilibrium bifurcation points may appear on the original sliding boundary line,which is divided into smaller parts,showing sliding and downward crossing dynamical characteristics.This is the root cause of the clusters,showing large-amplitude oscillations of relaxational type,resulting in the formation of mixed-mode fast-slow oscillations.Thus,a novel route to composite fast-slow dynamics by frequency switching is explained.Besides,the effects of the forcing on the mixed-mode fast-slow oscillations are explored.The magnitude of the forcing frequency may have some effects on the number of large-amplitude oscillations in the clusters.The magnitude of the forcing amplitude determines whether the fast-slow characteristics can be produced.展开更多
We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the ...We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.展开更多
The presence of particles on the surface of a tunnel slope renders it susceptible to erosion by waterflow,which is a major cause of soil and water loss.In this study,a nonlinear mathematical model and a mechanical equi...The presence of particles on the surface of a tunnel slope renders it susceptible to erosion by waterflow,which is a major cause of soil and water loss.In this study,a nonlinear mathematical model and a mechanical equilibrium model are developed to investigate the distribution offlowfields and particle motion characteristics of tunnel slopes,respectively.The mathematical model offlowfields comprises three parts:a runoff region,a highly permeable soil layer,and a weakly permeable soil layer.The Navier‒Stokes equation controlsfluid motion in the runoff region,while the Brinkman-extended Darcy equation governs fast and slow seepage in the highly and weakly permeable soil layers,respectively.Analytical solutions are derived for the velocity profile and shear stress expression of the modelflowfield under the boundary condition of continuous transition of velocity and stress at thefluid‒solid interface.The shear stress distribution shows that the shear stress at the tunnel-slope surface is the largest,followed by the shear stress of the soil interface,indicating that particles in these two locations are most vulnerable to erosion.A mechanical equilibrium model of sliding and rolling of single particles is established at thefluid‒solid interface,and the safety factor of particle motion(sliding and rolling)is derived.Sensitivity analysis shows that by increasing the runoff depth,slope angle,and soil permeability,the erosion of soil particles will be aggravated on the tunnel-slope surface,but by increasing the particle diameter,particle-specific gravity,and particle stacking angle,the erosion resistance ability of the tunnel-slope surface particles will be enhanced.This study can serve as a reference for the analysis of surface soil and water loss in tunnel-slope systems.展开更多
We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency win...We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency windows one by one, we analyze the physical mechanism through which each transparency window forms in detail. Additionally, we discuss how the system parameters affect the formation of transparency windows and conclude that the location, width, and absorption of each transparency window can be arbitrarily manipulated by varying the appropriate parameters. Moreover, when the pump field is changed from red to blue detuning, conversions between slow and fast light occur in the output field. These interesting properties of the output field can be applied to achieve the coherent control and manipulation of light pulses using cavity optomechanical system.展开更多
Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with r...Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12272150,12072132,12372093)。
文摘Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the previous work.The present paper aims to explore composite fast-slow dynamics when the frequency ratio is variable.As a result,a novel route to composite fast-slow dynamics is obtained.We find that,when presented with variable frequency ratios in a 1:n fashion,the sliding fast-slow oscillations may turn into the ones characterized by the fact that the clusters of large-amplitude oscillations of relaxational type are exhibited in each period of the oscillations,and hence the mixedmode fast-slow oscillations.Depending on whether the transition of the trajectory is from the upper subsystem via the fold bifurcation or not,these interesting oscillations are divided into two classes,both of which are investigated numerically.Our study shows that,when the frequency ratio n is increased from n=3,newly created boundary equilibrium bifurcation points may appear on the original sliding boundary line,which is divided into smaller parts,showing sliding and downward crossing dynamical characteristics.This is the root cause of the clusters,showing large-amplitude oscillations of relaxational type,resulting in the formation of mixed-mode fast-slow oscillations.Thus,a novel route to composite fast-slow dynamics by frequency switching is explained.Besides,the effects of the forcing on the mixed-mode fast-slow oscillations are explored.The magnitude of the forcing frequency may have some effects on the number of large-amplitude oscillations in the clusters.The magnitude of the forcing amplitude determines whether the fast-slow characteristics can be produced.
基金supported by NSF (1620449)NSFC (11531006 and 11771449)
文摘We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.
基金National Natural Science Foundation of China,Grant/Award Number:52109125Fundamental Research Funds for the Central Universities,Grant/Award Number:2023ZYGXZRx2tjD2231010Natural Science Foundation of Jiangsu Province,Grant/Award Number:BK20231217。
文摘The presence of particles on the surface of a tunnel slope renders it susceptible to erosion by waterflow,which is a major cause of soil and water loss.In this study,a nonlinear mathematical model and a mechanical equilibrium model are developed to investigate the distribution offlowfields and particle motion characteristics of tunnel slopes,respectively.The mathematical model offlowfields comprises three parts:a runoff region,a highly permeable soil layer,and a weakly permeable soil layer.The Navier‒Stokes equation controlsfluid motion in the runoff region,while the Brinkman-extended Darcy equation governs fast and slow seepage in the highly and weakly permeable soil layers,respectively.Analytical solutions are derived for the velocity profile and shear stress expression of the modelflowfield under the boundary condition of continuous transition of velocity and stress at thefluid‒solid interface.The shear stress distribution shows that the shear stress at the tunnel-slope surface is the largest,followed by the shear stress of the soil interface,indicating that particles in these two locations are most vulnerable to erosion.A mechanical equilibrium model of sliding and rolling of single particles is established at thefluid‒solid interface,and the safety factor of particle motion(sliding and rolling)is derived.Sensitivity analysis shows that by increasing the runoff depth,slope angle,and soil permeability,the erosion of soil particles will be aggravated on the tunnel-slope surface,but by increasing the particle diameter,particle-specific gravity,and particle stacking angle,the erosion resistance ability of the tunnel-slope surface particles will be enhanced.This study can serve as a reference for the analysis of surface soil and water loss in tunnel-slope systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.61822114,11465020,61465013,and 11264042)the Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project(Grant No.20160519022JH)
文摘We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency windows one by one, we analyze the physical mechanism through which each transparency window forms in detail. Additionally, we discuss how the system parameters affect the formation of transparency windows and conclude that the location, width, and absorption of each transparency window can be arbitrarily manipulated by varying the appropriate parameters. Moreover, when the pump field is changed from red to blue detuning, conversions between slow and fast light occur in the output field. These interesting properties of the output field can be applied to achieve the coherent control and manipulation of light pulses using cavity optomechanical system.
基金Project supported by the National Natural Science Foundation of China for Outstanding Youth(Grant No.51622906)the National Natural Science Foundation of China(Grant No.51479173)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.201304030577)the Scientific Research Funds of Northwest A&F University(Grant No.2013BSJJ095)the Science Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova Program,China(Grant No.2016KJXX-55)
文摘Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.
