在复数范围内讨论了Modified Korteweg de Vries(mKdV)方程孤立波解的结构.发现在一定参数情况下,该解的实部为反向或同向双峰孤立波而虚部为双扭结状孤立波(或反之).接着对文献中提出的有限差分格式进行了理论分析,表明其为二阶精度的...在复数范围内讨论了Modified Korteweg de Vries(mKdV)方程孤立波解的结构.发现在一定参数情况下,该解的实部为反向或同向双峰孤立波而虚部为双扭结状孤立波(或反之).接着对文献中提出的有限差分格式进行了理论分析,表明其为二阶精度的条件稳定格式,并解析地给出了数值稳定性条件.最后采用该格式对mKdV方程描述的该类波的动力学稳定性进行了数值研究,发现既存在动力学稳定的孤立波,也存在动力学不稳定的孤立波.展开更多
The interplay between chemistry and interfacial-tension-driven hydrodynamic instabilities has been studied experimentally. The system on hand consists of two immiscible liquids separated along an initially plane inter...The interplay between chemistry and interfacial-tension-driven hydrodynamic instabilities has been studied experimentally. The system on hand consists of two immiscible liquids separated along an initially plane interface at which an interfacial reaction takes place to produce in situ a surfactant. It is identified that the dynamics of the system depends on the orientation of the Hele-Shaw cell with respect to the vector of gravity. If the nele-Shaw cell is placed vertically, Marangoni cells with vigorous convection develop in both phases along a nearly planar interface. However, if the Hele-Shaw cell is tilted off the gravity, the instabilities in the system are characterized by the large scale interracial deformation with a spatio-temporal periodicity together with the chemo-Marangoni convection. The focus is on the exploration of the transition from the cellular mode to the large scale interfacial deformation.展开更多
A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major fac...A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major factors that can affect low-speed instability.The mathematic model was established to obtain the change rule of speed andinstantaneous acceleration of the hydraulic motor.Then, Matlab was used to simulate theeffect of nonlinear friction force and hydraulic motor parameters such as coefficient of leakand compression ratio, etc., under low speed.Finally, some measures were proposed toimprove the low-speed stability of the hydraulic motor.展开更多
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin...Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.展开更多
The aim of this work is to investigate the flow instabilities in a baffled, stirred tank generated by a single Rushton turbine by means of large eddy simulation （LES）. The sliding mesh method was used for the coupli...The aim of this work is to investigate the flow instabilities in a baffled, stirred tank generated by a single Rushton turbine by means of large eddy simulation （LES）. The sliding mesh method was used for the coupling between the rotating and the stationary frame of references. The calculations were carried out on the ＂Shengcao-21C＂ supercomputer using a computational fluid dynamics （CFD） code CFX5. The flow fields predicted by the LES simulation and the simulation using standard κ-ε model were compared to the results from particle image velocimetry （PIV） measurements. It is shown that the CFD simulations using the LES approach and the standard κ-ε model agree well with the PIV measurements. Fluctuations of the radial and axial velocity are predicted at different frequencies by the LES simulation. Velocity fluctuations of high frequencies are seen in the impeller region, while low frequencies velocity fluctuations are observed in the bulk flow. A low frequency velocity fluctuation with a nondimensional frequency of 0.027Hz is predicted by the LES simulation, which agrees with experimental investigations in the literature. Flow circulation patterns predicted by the LES simulation are asymmetric, stochastic and complex, spanning a large portion of the tanks and varying with time, while circulation patterns calculated by the simulation using the standard κ-ε model are symmetric. The results of the present work give better understanding to the flow instabilities in the mechanically agitated tank. However, further analysis of the LES calculated velocity series by means of fast Fourier transform （FFT） and/or spectra analysis are recommended in future work in order to gain more knowledge of the complicated flow phenomena.展开更多
An essential dispersion relation,which can describe the dynamic properties of stimulated Raman scattering instability as a laser beam propagates through plasmas,is derived analytically.The development of growth mode,a...An essential dispersion relation,which can describe the dynamic properties of stimulated Raman scattering instability as a laser beam propagates through plasmas,is derived analytically.The development of growth mode,angle distribution,and temperature dependence of the instabilities are presented by solving this dispersion relation numerically.A significant dynamic characteristic has been revealed that the temperature increasing of the electron would result in redshift of scattered spectrum at high laser intensities.Furthermore,a novel modulational instability with double-peak temporal structure appears in a limited density region because of the coupling of scattered upshift and downshift waves.展开更多
Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk ...Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease(PD).Recently,analytical techniques,inspired by the dynamical systems perspective on movement control and coordination,have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.Methods:A wavelet-based technique was used to identify limit cycle oscillations(LCOs) in the anterior–posterior(AP) postural sway of people with mild PD(n = 10) compared to age-matched controls(n = 10).Participants stood on a foam and on a rigid surface while completing a dual task(speaking).Results:There was no significant difference in the root mean square of center of pressure between groups.Three out of 10 participants with PD demonstrated LCOs on the foam surface,while none in the control group demonstrated LCOs.An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain.Conclusion:Overall,the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD.In addition,these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.展开更多
文摘在复数范围内讨论了Modified Korteweg de Vries(mKdV)方程孤立波解的结构.发现在一定参数情况下,该解的实部为反向或同向双峰孤立波而虚部为双扭结状孤立波(或反之).接着对文献中提出的有限差分格式进行了理论分析,表明其为二阶精度的条件稳定格式,并解析地给出了数值稳定性条件.最后采用该格式对mKdV方程描述的该类波的动力学稳定性进行了数值研究,发现既存在动力学稳定的孤立波,也存在动力学不稳定的孤立波.
基金Deutsche Forschung Gemainschaft(Ec/201/1-5)Deutsches Zentrum fuer Luft und Raumfahrt(50WM0058).
文摘The interplay between chemistry and interfacial-tension-driven hydrodynamic instabilities has been studied experimentally. The system on hand consists of two immiscible liquids separated along an initially plane interface at which an interfacial reaction takes place to produce in situ a surfactant. It is identified that the dynamics of the system depends on the orientation of the Hele-Shaw cell with respect to the vector of gravity. If the nele-Shaw cell is placed vertically, Marangoni cells with vigorous convection develop in both phases along a nearly planar interface. However, if the Hele-Shaw cell is tilted off the gravity, the instabilities in the system are characterized by the large scale interracial deformation with a spatio-temporal periodicity together with the chemo-Marangoni convection. The focus is on the exploration of the transition from the cellular mode to the large scale interfacial deformation.
基金Supported by the Natural Science Foundation of Fujian Province of China(2009J01259)Scientific Research Foundation of Department of Education(JB08182)
文摘A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major factors that can affect low-speed instability.The mathematic model was established to obtain the change rule of speed andinstantaneous acceleration of the hydraulic motor.Then, Matlab was used to simulate theeffect of nonlinear friction force and hydraulic motor parameters such as coefficient of leakand compression ratio, etc., under low speed.Finally, some measures were proposed toimprove the low-speed stability of the hydraulic motor.
文摘Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.
文摘The aim of this work is to investigate the flow instabilities in a baffled, stirred tank generated by a single Rushton turbine by means of large eddy simulation （LES）. The sliding mesh method was used for the coupling between the rotating and the stationary frame of references. The calculations were carried out on the ＂Shengcao-21C＂ supercomputer using a computational fluid dynamics （CFD） code CFX5. The flow fields predicted by the LES simulation and the simulation using standard κ-ε model were compared to the results from particle image velocimetry （PIV） measurements. It is shown that the CFD simulations using the LES approach and the standard κ-ε model agree well with the PIV measurements. Fluctuations of the radial and axial velocity are predicted at different frequencies by the LES simulation. Velocity fluctuations of high frequencies are seen in the impeller region, while low frequencies velocity fluctuations are observed in the bulk flow. A low frequency velocity fluctuation with a nondimensional frequency of 0.027Hz is predicted by the LES simulation, which agrees with experimental investigations in the literature. Flow circulation patterns predicted by the LES simulation are asymmetric, stochastic and complex, spanning a large portion of the tanks and varying with time, while circulation patterns calculated by the simulation using the standard κ-ε model are symmetric. The results of the present work give better understanding to the flow instabilities in the mechanically agitated tank. However, further analysis of the LES calculated velocity series by means of fast Fourier transform （FFT） and/or spectra analysis are recommended in future work in order to gain more knowledge of the complicated flow phenomena.
文摘An essential dispersion relation,which can describe the dynamic properties of stimulated Raman scattering instability as a laser beam propagates through plasmas,is derived analytically.The development of growth mode,angle distribution,and temperature dependence of the instabilities are presented by solving this dispersion relation numerically.A significant dynamic characteristic has been revealed that the temperature increasing of the electron would result in redshift of scattered spectrum at high laser intensities.Furthermore,a novel modulational instability with double-peak temporal structure appears in a limited density region because of the coupling of scattered upshift and downshift waves.
基金the National Science Foundation for partial financial support for this project provided through the grant CMMI-1300632Purdue University for partial financial support for this project through a Research Incentive Grant
文摘Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease(PD).Recently,analytical techniques,inspired by the dynamical systems perspective on movement control and coordination,have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.Methods:A wavelet-based technique was used to identify limit cycle oscillations(LCOs) in the anterior–posterior(AP) postural sway of people with mild PD(n = 10) compared to age-matched controls(n = 10).Participants stood on a foam and on a rigid surface while completing a dual task(speaking).Results:There was no significant difference in the root mean square of center of pressure between groups.Three out of 10 participants with PD demonstrated LCOs on the foam surface,while none in the control group demonstrated LCOs.An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain.Conclusion:Overall,the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD.In addition,these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.
