In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of...In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation (SDDPE) is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.展开更多
Ultrasonic vibration can reduce the forming force, decrease the friction in the metal forming process and improve the surface quality of the workpiece effectively. Tensile tests of AZ31 magnesium alloy were carried ou...Ultrasonic vibration can reduce the forming force, decrease the friction in the metal forming process and improve the surface quality of the workpiece effectively. Tensile tests of AZ31 magnesium alloy were carried out. The stress–strain relationship, fracture modes of tensile specimens, microstructure and microhardness under different vibration conditions were analyzed, in order to study the effects of the ultrasonic vibration on microstructure and performance of AZ31 magnesium alloy under tensile deformation. The results showed that the different reductions of the true stress appeared under various ultrasonic vibration conditions, and the maximum decreasing range was 4.76%. The maximum microhardness difference among the 3 nodes selected along the specimen was HV 10.9. The fracture modes, plasticity and microstructure of AZ31 magnesium alloy also were affected by amplitude and action time of the ultrasonic vibration. The softening effect and the hardening effect occurred simultaneously when the ultrasonic vibration was applied. When the ultrasonic amplitude was 4.6 μm with short action time, the plastic deformation was dominated by twins and the softening effect was dominant. However, the twinning could be inhibited and the hardening effect became dominant in the case of high ultrasonic energy.展开更多
A parameter, known as the parameter of humidification vibration deformation, was proposed, describing quantitatively the impact of water content on vibration settlement deformation, and its relationship with humidific...A parameter, known as the parameter of humidification vibration deformation, was proposed, describing quantitatively the impact of water content on vibration settlement deformation, and its relationship with humidification water content, dynamic shear stress peak value, initial consolidation stress and vibration frequency was built. The result shows that 1) the parameter of humidification vibration deformation increases with the vibration shear stress peak value increasing. 2) The humidification water content has significant influence on the curve of the parameter of humidification vibration deformation and the peak vibration shear stress. When the humidification water content is low, the curve increases slowly. However, when the humidification water content is high, the curve increases rapidly. 3) Initial consolidation stress has significant influence on the humidification vibration deformation coefficient. When initial consolidation stress is not large enough to destroy the loess structure, with initial consolidation stress increasing, the humidification vibration deformation coefficient decreases. On the contrary, the humidification vibration deformation coefficient increases with initial consolidation stress increasing. 4) With the increase of vibration time, the parameter of humidification vibration settlement shows an increasing trend overall. The initial dynamic shear stress peak value and humidification water content all have significant effects on the curve of the parameter of humidification vibration settlement and vibration time. However, the humidification water content is even more significant.展开更多
The vibration behavior of the ground and houses caused by monorail traffic is discussed in this paper. The environmental ground vibration problem discussed herein occurs in a residential area near a monorail used for ...The vibration behavior of the ground and houses caused by monorail traffic is discussed in this paper. The environmental ground vibration problem discussed herein occurs in a residential area near a monorail used for public transportation, Vibrations were measured on the ground at the side of monorail piers lacing the residential area and within the affected houses. Results indicate that the vibration level in the house was 60 dB or more, a level high enough to warrant complaints, Peculiar geological and geographical features are thought to contribute to the amplification of low frequency (-10 Hz) ground vibrations to irritable levels in these homes even though a distance of≥30 m separates the residential area and the monorail.展开更多
Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 (2007) 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. ...Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 (2007) 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity k, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.展开更多
Asymptotic behavior of the scattering amplitude for two scalar particles at high energy and fixed momentum transfer is reconsidered in quantum field theory. In the framework of the quasi-potential approach and the mod...Asymptotic behavior of the scattering amplitude for two scalar particles at high energy and fixed momentum transfer is reconsidered in quantum field theory. In the framework of the quasi-potential approach and the modified perturbation theory, a systematic scheme for finding the leading eikonal scattering amplitudes and its corrections are developed and constructed. The differential cross section is also discussed.展开更多
The dynamic behavior of the entanglement for the pair cat states in the amplitude decoherence channel isstudied by adopting the entanglement of formation determined by the concurrence.Then,we consider the teleportatio...The dynamic behavior of the entanglement for the pair cat states in the amplitude decoherence channel isstudied by adopting the entanglement of formation determined by the concurrence.Then,we consider the teleportationby using joint measurements of the photon-number sum and phase difference with the pair cat states as an entangleresource and discuss the influence of amplitude decoherence on the mean fidelity of the teleportation.展开更多
The dynamic behaviour of power line cables have been a source of interest to researchers ever since the phenomenon was first noticed in the 1920s. Conductor oscillation is mostly caused by the dynamic forces of nature...The dynamic behaviour of power line cables have been a source of interest to researchers ever since the phenomenon was first noticed in the 1920s. Conductor oscillation is mostly caused by the dynamic forces of nature such as wind loading. This imposes a periodic force on the conductors which is highly undesirable. It is therefore important for engineers to account for the possible effect of the wind loading when designing the power line. Investigations have shown that modeling the exact dynamic behaviour of a conductor is very difficult. Based on this fact, getting the exact analytical solution to conductor vibration is difficult, which is almost impossible, hence the numerical approximation becomes an option. This paper presents the developed finite element method used to analyse the dynamic behaviour of transmission line conductors. The developed FEM (finite element method) is implemented on MATLAB. The numerical analysis using MATLAB that is presented in this paper is used to simulate the response of the conductor when subjected to external loading in the time domain. The simulation is used to analyse the transverse vibration of the conductor. The formulation of the stiffness matrix and load vector is done and the results obtained are used to evaluate the conductor's internal energy dissipation. This finite element solution is compared with the results documented in literature. This numerical simulation is also used to investigate the effects of varying the axial tension on energy dissipation within the strands. Hence, this evolved in physically appropriate energy characterization process that can be used to evaluate the conductor self-damping with respect to line contact.展开更多
This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases wh...This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases where known results fail to apply.The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale.These criteria improve a number of related contributions to the subject.Some illustrative examples are provided.展开更多
This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed ...This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.展开更多
Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis...Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.展开更多
Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entra...Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entrainment against cavitation erosion has been paid good attention to. In the present work, the effect of air bubble size on cavitation erosion reduction was experimentally investigated. A device with micron-scale orifice diameters(10, 20 and 50 μm in size) was specially designed to introduce air bubbles into water. The experiments about the effect of air bubble size were conducted by means of a vibratory apparatus, including the behavior of formation and movement for single air bubble, the characteristics of cavitation erosion reduction at different air entrainment conditions. The findings demonstrate that high air concentration has significant effects on cavitation erosion reduction.But, a notable problem was that the size of air bubbles is of outstanding effect on cavitation erosion reduction. Small air bubbles support to alleviate cavitation erosion, even at same air concentration.展开更多
Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski ga...Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpinski fractal as, for instance, a compact embedding result due to Fukushima and Shima.展开更多
The generic phantom bursting model proposed by Bertram et al.can evoke complex bursting oscillations in collaboration with two generic slow variables with different time scales.Two models with the phantom bursting mec...The generic phantom bursting model proposed by Bertram et al.can evoke complex bursting oscillations in collaboration with two generic slow variables with different time scales.Two models with the phantom bursting mechanism are suggested,when these two generic slow variables are provided with some specific biological significances by combining slowly varying intracellular Ca2+concentration of the Chay-Keizer electrical bursting model with two different glycolytic oscillations,respectively.Also,complex dynamic behaviors of different compound bursting occurring in these two models are comprehensively surveyed by two fast/slow analyses for a moderately and a slower slow variable,respectively.展开更多
We carried out direct numerical simulations of turbulent Rayleigh-Benard convection(RBC)with accounting for both the roughness and the external vibration over the Rayleigh number range 10^(7)≤Ra≤10^(11) and the vibr...We carried out direct numerical simulations of turbulent Rayleigh-Benard convection(RBC)with accounting for both the roughness and the external vibration over the Rayleigh number range 10^(7)≤Ra≤10^(11) and the vibration frequency range 0<ω<1400.The triangular rough elements are uniformly distributed over the top and bottom surfaces,and the vibration is applied in the horizontal direction.It is shown that under the combined action of roughness and horizontal vibration,with increasing the vibration frequency ω,the heat transfer is initially decreased a little and then greatly enhanced after ω exceeds the critical value.The physical reason for massive heat-transfer-enhancement is that high frequency vibration destabilizes thermal boundary layers(BL)over rough surfaces,triggers abundant emissions of thermal plumes,and strengthens the motion of large-scale circulation(LSC),which consequently thins the thickness of thermal BL and heightens the convective transport.In addition,it is shown that vibration-induced heat-transfer-enhancement can obviously affect the scaling behavior between the heat flux and the Rayleigh number,and the scaling exponent increases with increasing ω,whereas the influence of vibration on the scaling behavior between the intensity of LSC and Ra is very weak.展开更多
This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral ave...This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral averaging technique,new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation.Our results generalize and improve some known theorems.展开更多
文摘In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation (SDDPE) is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.
基金Projects(51375269,51675307) supported by the National Natural Science Foundation of China
文摘Ultrasonic vibration can reduce the forming force, decrease the friction in the metal forming process and improve the surface quality of the workpiece effectively. Tensile tests of AZ31 magnesium alloy were carried out. The stress–strain relationship, fracture modes of tensile specimens, microstructure and microhardness under different vibration conditions were analyzed, in order to study the effects of the ultrasonic vibration on microstructure and performance of AZ31 magnesium alloy under tensile deformation. The results showed that the different reductions of the true stress appeared under various ultrasonic vibration conditions, and the maximum decreasing range was 4.76%. The maximum microhardness difference among the 3 nodes selected along the specimen was HV 10.9. The fracture modes, plasticity and microstructure of AZ31 magnesium alloy also were affected by amplitude and action time of the ultrasonic vibration. The softening effect and the hardening effect occurred simultaneously when the ultrasonic vibration was applied. When the ultrasonic amplitude was 4.6 μm with short action time, the plastic deformation was dominated by twins and the softening effect was dominant. However, the twinning could be inhibited and the hardening effect became dominant in the case of high ultrasonic energy.
基金Foundation item: Project(51178392) supported by the National Natural Science Foundation of China
文摘A parameter, known as the parameter of humidification vibration deformation, was proposed, describing quantitatively the impact of water content on vibration settlement deformation, and its relationship with humidification water content, dynamic shear stress peak value, initial consolidation stress and vibration frequency was built. The result shows that 1) the parameter of humidification vibration deformation increases with the vibration shear stress peak value increasing. 2) The humidification water content has significant influence on the curve of the parameter of humidification vibration deformation and the peak vibration shear stress. When the humidification water content is low, the curve increases slowly. However, when the humidification water content is high, the curve increases rapidly. 3) Initial consolidation stress has significant influence on the humidification vibration deformation coefficient. When initial consolidation stress is not large enough to destroy the loess structure, with initial consolidation stress increasing, the humidification vibration deformation coefficient decreases. On the contrary, the humidification vibration deformation coefficient increases with initial consolidation stress increasing. 4) With the increase of vibration time, the parameter of humidification vibration settlement shows an increasing trend overall. The initial dynamic shear stress peak value and humidification water content all have significant effects on the curve of the parameter of humidification vibration settlement and vibration time. However, the humidification water content is even more significant.
文摘The vibration behavior of the ground and houses caused by monorail traffic is discussed in this paper. The environmental ground vibration problem discussed herein occurs in a residential area near a monorail used for public transportation, Vibrations were measured on the ground at the side of monorail piers lacing the residential area and within the affected houses. Results indicate that the vibration level in the house was 60 dB or more, a level high enough to warrant complaints, Peculiar geological and geographical features are thought to contribute to the amplification of low frequency (-10 Hz) ground vibrations to irritable levels in these homes even though a distance of≥30 m separates the residential area and the monorail.
基金supported by the National Natural Science Foundation of China under Grant No.10575041
文摘Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 (2007) 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity k, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.
文摘Asymptotic behavior of the scattering amplitude for two scalar particles at high energy and fixed momentum transfer is reconsidered in quantum field theory. In the framework of the quasi-potential approach and the modified perturbation theory, a systematic scheme for finding the leading eikonal scattering amplitudes and its corrections are developed and constructed. The differential cross section is also discussed.
基金Supported by National Natural Science Foundation of China under Grant No.10774143the National Key Project for Fundamental Research of China under Grant No.2006CB921403
文摘The dynamic behavior of the entanglement for the pair cat states in the amplitude decoherence channel isstudied by adopting the entanglement of formation determined by the concurrence.Then,we consider the teleportationby using joint measurements of the photon-number sum and phase difference with the pair cat states as an entangleresource and discuss the influence of amplitude decoherence on the mean fidelity of the teleportation.
文摘The dynamic behaviour of power line cables have been a source of interest to researchers ever since the phenomenon was first noticed in the 1920s. Conductor oscillation is mostly caused by the dynamic forces of nature such as wind loading. This imposes a periodic force on the conductors which is highly undesirable. It is therefore important for engineers to account for the possible effect of the wind loading when designing the power line. Investigations have shown that modeling the exact dynamic behaviour of a conductor is very difficult. Based on this fact, getting the exact analytical solution to conductor vibration is difficult, which is almost impossible, hence the numerical approximation becomes an option. This paper presents the developed finite element method used to analyse the dynamic behaviour of transmission line conductors. The developed FEM (finite element method) is implemented on MATLAB. The numerical analysis using MATLAB that is presented in this paper is used to simulate the response of the conductor when subjected to external loading in the time domain. The simulation is used to analyse the transverse vibration of the conductor. The formulation of the stiffness matrix and load vector is done and the results obtained are used to evaluate the conductor's internal energy dissipation. This finite element solution is compared with the results documented in literature. This numerical simulation is also used to investigate the effects of varying the axial tension on energy dissipation within the strands. Hence, this evolved in physically appropriate energy characterization process that can be used to evaluate the conductor self-damping with respect to line contact.
基金supported by National Key Basic Research Program of China (Grant No. 2013CB035604)National Natural Science Foundation of China (Grant Nos. 61034007, 51277116 and51107069)
文摘This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases where known results fail to apply.The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale.These criteria improve a number of related contributions to the subject.Some illustrative examples are provided.
基金supported by the National Natural Science Foundation of China(Grant No.10632040)
文摘This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.
基金supported by the National Natural Science Foundation of China (Grant No. 60971090)the Natural Science Foundations of Jiangsu Province, China (Grant No. BK2009105)
文摘Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.
基金supported by the National Natural Science Foundation of China(Grant No.51409187)the Fundamental Research Funds for the Central Universities(Grant No.2016B09914)
文摘Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entrainment against cavitation erosion has been paid good attention to. In the present work, the effect of air bubble size on cavitation erosion reduction was experimentally investigated. A device with micron-scale orifice diameters(10, 20 and 50 μm in size) was specially designed to introduce air bubbles into water. The experiments about the effect of air bubble size were conducted by means of a vibratory apparatus, including the behavior of formation and movement for single air bubble, the characteristics of cavitation erosion reduction at different air entrainment conditions. The findings demonstrate that high air concentration has significant effects on cavitation erosion reduction.But, a notable problem was that the size of air bubbles is of outstanding effect on cavitation erosion reduction. Small air bubbles support to alleviate cavitation erosion, even at same air concentration.
基金supported by Grant CNCS PCE 47/2011 (Qualitative and Numerical Analysis of Nonlinear Problems on Fractals)supported by the GNAMPA Project(Esistenza e molteplicit di soluzioni per problemi differenziali non lineari) 2012
文摘Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpinski fractal as, for instance, a compact embedding result due to Fukushima and Shima.
基金supported by the National Natural Science Foundation of China(Grant Nos.1137201711072013 and 11202083)
文摘The generic phantom bursting model proposed by Bertram et al.can evoke complex bursting oscillations in collaboration with two generic slow variables with different time scales.Two models with the phantom bursting mechanism are suggested,when these two generic slow variables are provided with some specific biological significances by combining slowly varying intracellular Ca2+concentration of the Chay-Keizer electrical bursting model with two different glycolytic oscillations,respectively.Also,complex dynamic behaviors of different compound bursting occurring in these two models are comprehensively surveyed by two fast/slow analyses for a moderately and a slower slow variable,respectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.11988102,92052201,91852202,H825204,and 11972220)the Program of Shanghai Academic Research Leader(Grant No.19XD1421400)+1 种基金Shanghai Science and Technology Program(Grant Nos.19JC1412802 and 20ZR14I9800)China Postdoctoral Science Foundation(Grant No.2020M681259).
文摘We carried out direct numerical simulations of turbulent Rayleigh-Benard convection(RBC)with accounting for both the roughness and the external vibration over the Rayleigh number range 10^(7)≤Ra≤10^(11) and the vibration frequency range 0<ω<1400.The triangular rough elements are uniformly distributed over the top and bottom surfaces,and the vibration is applied in the horizontal direction.It is shown that under the combined action of roughness and horizontal vibration,with increasing the vibration frequency ω,the heat transfer is initially decreased a little and then greatly enhanced after ω exceeds the critical value.The physical reason for massive heat-transfer-enhancement is that high frequency vibration destabilizes thermal boundary layers(BL)over rough surfaces,triggers abundant emissions of thermal plumes,and strengthens the motion of large-scale circulation(LSC),which consequently thins the thickness of thermal BL and heightens the convective transport.In addition,it is shown that vibration-induced heat-transfer-enhancement can obviously affect the scaling behavior between the heat flux and the Rayleigh number,and the scaling exponent increases with increasing ω,whereas the influence of vibration on the scaling behavior between the intensity of LSC and Ra is very weak.
基金Supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2010AM031 and ZR2011AL001the Development Program in Science and Technology of Shandong Province of China under Grant No. 2010GWZ20401
文摘This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral averaging technique,new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation.Our results generalize and improve some known theorems.