Investigation of the unstable flow phenomenon in a pump turbine

Instability of pump turbine with S-shaped curve is characterized by large fluctuations of rotational speed during the transient processes.For investigating this phenomenon,a numerical model based on the dynamic sliding mesh method(DSSM)is presented and used to numerically solve the 3D transient flow which is characterized by the variable rotation speed of runner.The method is validated by comparison with measured data for a load rejection process in a prototype pump turbine.The results show that the calculated rotation speed agrees well with the experimental data.Based on the validated model,simulations were performed for the runaway process using an artificially assumed operating condition under which the unstable rotation speed is expected to appear.The results confirm that the instability of runner rotational speed can be effectively captured with the proposed method.Presented results include the time history profiles of unit flow rate and unit rotating speed.The internal flow characteristics in a typical unstable period are discussed in detail and the mechanism of the unstable hydraulic phenomenon is explained.Overall,the results suggest that the method presented here can be a viable alternative to predict the dynamic characteristics of pump turbines during transient processes.     

A General Random Walk Model of Molecular Motor

A general random walk model framework is presented which can be used to statistically describe the internal dynamics and external mechanical movement of molecular motors along filament track. The motion of molecular motor in a periodic potential and a constant force is considered. We show that the molecular motor‘s movement becomes slower with the potential barrier increasing, but if the force is increased, the molecular motor‘‘s movement becomes faster. The relation between the effective rate constant and the potential battler‘s height, and that between the effective rate constant and the value of the force are discussed. Our results are consistent with the experiments and relevant theoretical consideration, and can be used to explain some physiological phenomena.     

Effects of rebinding rate and asymmetry in unbinding rate on cargo transport by multiple kinesin motors

Many intracellular transports are performed by multiple molecular motors in a cooperative manner.Here,we use stochastic simulations to study the cooperative transport by multiple kinesin motors,focusing mainly on effects of the form of unbinding rate versus force and the rebinding rate of single motors on the cooperative transport.We consider two forms of the unbinding rate.One is the symmetric form with respect to the force direction,which is obtained according to Kramers theory.The other is the asymmetric form,which is obtained from the prior studies for the single kinesin motor.With the asymmetric form the simulated results of both velocity and run length of the cooperative transport by two identical motors and those by a kinesin-1 motor and a kinesin-2 motor are in quantitative agreement with the available experimental data,whereas with the symmetric form the simulated results are inconsistent with the experimental data.For the cooperative transport by a faster motor and a much slower motor,the asymmetric form can give both larger velocity and longer run length than the symmetric form,giving an explanation for why kinesin adopts the asymmetric form of the unbinding rate rather than the symmetric form.For the cooperative transport by two identical motors,while the velocity is nearly independent of the rebinding rate,the run length increases linearly with the rebinding rate.For the cooperative transport by two different motors,the increase of the rebinding rate of one motor also enhances the run length of the cooperative transport.The dynamics of transport by N(N=3,4,5,6,7 and 8)motors is also studied.     

Collective effects for long bunches in dual harmonic RF systems

The storage of long bunches for large time intervals needs flattened stationary buckets with a large bucket height. Collective effects from the space charge and resistive impedance are studied by looking at the incoherent particle motion for the matched and mismatched bunches. Increasing the RF amplitude with particle number provides r.m.s wise matching for modest intensities. The incoherent motion of large amplitude particles depends on the details of the RF system. The resulting debunching process is a combination of the too small full RF acceptance together with the mismatch, enhanced by the collective effects. Irregular single particle motion is not associated with the coherent dipole instability. For the stationary phase space distribution of the Hofmann-Pedersen approach and for the dual harmonic RF system, stability limits are presented, which are too low if using realistic input distributions. For single and dual harmonic RF system with $d$=0.31, the tracking results are shown for intensities, by a factor of 3 above the threshold values. Small resistive impedances lead to coherent oscillations around the equilibrium phase value, as energy loss by resistive impedance is compensated by the energy gain of the RF system.     

Monte-Carlo Simulation of Multiple-Molecular-Motor Transport

Multimotor transport is studied by Monte-Carlo simulation with consideration of motor detachment from the filament. Our work shows, in the case of low load, the velocity of multi-motor system can decrease or increase with increasing motor numbers depending on the single motor force-velocity curve. The stall force and run-length reduced greatly compared to other models. Especially in the case of low ATP concentrations, the stall force of multi motor transport even smaller than the single motor＇s stall force.     

Influence of dark energy on time-like geodesic motion in Schwarzschild spacetime

In this paper we investigate the influence of the dark energy on the time-like geodesic motion of a particle in Schwarzschild spacetime by analysing the behaviour of the effective potential which appears in an equation of motion. For the non-radial time-like geodesics, we find a bound orbit when the particle energy is in an appropriate range, and also find another possible orbit, which is that the particle drops straightly into the singularity of a black hole or escapes to infinity. For the radial time-like geodesics, we find an unstable circular orbit when the particle energy is the critical value, in which case it is possible for the particle to escape to infinity.     

Oscillations and Collapses of Proto--Neutron Stars

We examine the oscillation and collapse of a relativistic star, e.g., a proto-neutron star, with an equation of state （EOS） which is Mowly changing as driven by, e.g., losing of thermal energy through radiations. We find that the frequency of the fundamental mode of oscillation （radial） will gradually increase then abruptly drop to zero when the star gets close to the point of instability. We also find that for a wide range of configurations on the unstable branch of equilibrium configurations, the collapse is dominated by one unstable mode.     

Molecular dynamics simulations on the dynamics of two-dimensional rounded squares

The collective motion of rounded squares with different corner-roundness ζ is studied by molecular dynamics(MD)simulation in this work. Three types of translational collective motion pattern are observed, including gliding, hopping and a mixture of gliding and hopping. Quantitatively, the dynamics of each observed ordered phase is characterized by both mean square displacement and van Hove functions for both translation and rotation. The effect of corner-roundness on the dynamics is further studied by comparing the dynamics of the rhombic crystal phases formed by different corner-rounded particles at a same surface fraction. The results show that as ζ increases from 0.286 to 0.667, the translational collective motion of particles changes from a gliding-dominant pattern to a hopping-dominant pattern, whereas the rotational motion pattern is hopping-like and does not change in its type, but the rotational hopping becomes much more frequent as ζincreases(i.e., as particles become more rounded). A simple geometrical model is proposed to explain the trend of gliding motion observed in MD simulations.     

Dynamic Behaviour of Nanoscale Electrostatic Actuators

The dynamic behaviour for nanoscale electrostatic actuators is studied. A two parameter mass-spring model is shown to exhibit a bifurcation from the case excluding an equilibrium point to the case including two equilibrium points as the geometrical dimensions of the device are altered. Stability analysis shows that one is a stable Hopf bifurcation point and the other is an unstable saddle point. In addition, we plot the diagram phases, which have periodic orbits around the Hopf point and a homoclinic orbit passing though the unstable saddle point.     

Longitudinal instability caused by long drifts in the C-ADS injector-Ⅰ

The period length is usually much larger than the cavity effective length in a low energy superconducting linac.The long drifts between cavities will not only decrease the acceptance of the linac, but also lead to possible instability. The linac will be more sensitive to mismatch and other perturbations. From the longitudinal motion equation, the function which describes the parametric resonance is deduced and the relation between the instability region and the cavity filling factor is discussed. It indicates that if the zero current phase advance per period is kept below 90°, instability driven by parametric resonance will never occur. The space charge effect will enhance the instability, so that a stricter limitation on the phase advance per cell is required. From the numerical simulation results for two different schemes of Injector-Ⅰ of the C-ADS driver linac, one can find that even with just three cells in the unstable region, significant emittance growth can be observed. Further investigations show that it is apt to produce halo particles under resonance, and the machine becomes more sensitive to errors and mismatches. Therefore, it is important to keep all cells in the stable region throughout the linac of very high beam power to minimize beam losses.     

Elastically coupled molecular motors

We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays. Received: 27 November 1997 / Revised: 20 February 1998 / Accepted: 27 March 1998     

Collective dynamics of interacting molecular motors

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N> or approximately 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.     

Motor proteins transporting cargos

Processive motor proteins such as kinesin and myosin-V are enzymes that use the energy of ATP hydrolysis to travel along polar cytoskeletal filaments. One of the functions of these proteins is the transport of vesicles and protein complexes that are linked to the light chains of the motors. Modeling the light chain by a linear elastic spring, and using the two-state model for one- and two-headed molecular motors, we study the influence of thermal fluctuations of the cargo on the motion of the motor-cargo complex. We solve numerically the Fokker-Planck equations of motor motion, and find that the mean velocity of the motor-cargo complex decreases monotonously as the spring becomes softer. This effect is due to the random force of thermal fluctuations of the cargo disrupting the operation of the motor. Increasing the size (thus, the friction coefficient) of the cargo also decreases the velocity. Surprisingly, we find that for a given size of the cargo, the velocity has a maximum for a certain friction of the motor. We explain this effect by the interplay between the characteristic length of thermal fluctuations of the cargo on a spring, the motor diffusion length, and the filament period. Our results may be relevant for the interpretation of single-molecule experiments with molecular motors (bead assays), where the motor motion is observed by tracking of a bead attached to the motor.     

Theoretical analysis of a non-contact spring with inclined permanent magnets for load-independent resonance frequency

In this paper a non-contact magnetic spring design is presented that uses inclined magnets to produce an adjustable relationship between load force and dynamic stiffness. With appropriate choice of parameters, the spring may either operate with a range of constant natural frequency against variable load forces, or a positive stiffness in one horizontal direction may be achieved in addition to having a positive vertical stiffness. Dynamic simulations are presented to assess the non-linear stability of a planar three degree of freedom version of the system; cross-coupling between horizontal and rotation motion is shown to compromise passive stability, in which case passive constraints or active control must be used to avoid instability. The design is scalable in that using larger magnets increases the load bearing capacity and decreases the natural frequency of the system.     

Nonlinear parametric instability of wind turbine wings

Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability of a wind turbine wing has been analysed based on a two-degrees-of-freedom model with one modal coordinate representing the vibrations in the blade direction and the other vibrations in edgewise direction. The functional basis for the eigenmode expansion has been taken as the linear undamped fixed-base eigenmodes. It turns out that the system becomes unstable at certain excitation amplitudes and frequencies. If the ratio between the support point motion and the rotational frequency of the rotor is rational, the response becomes periodic, and Floquet theory may be used to determine instability. In reality the indicated frequency ratio may be irrational in which case the response is shown to be quasi-periodic, rendering the Floquet theory useless. Moreover, as the excitation frequency exceeds the eigenfrequency in the edgewise direction, the response may become chaotic. For this reason stability of the system has in all cases been evaluated based on a Lyapunov exponent approach. Stability boundaries are determined as a function of the amplitude and frequency of the support point motion, the rotational speed, damping ratios and eigenfrequencies in the blade and edgewise directions.     

Instabilities in a two-dimensional polar-filament-motor system

The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.     

Chains of oscillators with negative stiffness elements

Negative stiffness is not allowed by thermodynamics and hence materials and systems whose global behaviour exhibits negative stiffness are unstable. However the stability is possible when these materials/systems are elements of a larger system sufficiently stiff to stabilise the negative stiffness elements. In order to investigate the effect of stabilisation we analyse oscillations in a chain of n linear oscillators (masses and springs connected in series) when some of the springs? stiffnesses can assume negative values. The ends of the chain are fixed. We formulated the necessary stability condition: only one spring in the chain can have negative stiffness. Furthermore, the value of negative stiffness cannot exceed a certain critical value that depends upon the (positive) stiffnesses of other springs. At the critical negative stiffness the system develops an eigenmode with vanishing frequency. In systems with viscous damping vanishing of an eigenfrequency does not yet lead to instability. Further increase in the value of negative stiffness leads to the appearance of aperiodic eigenmodes even with light damping. At the critical negative stiffness the low dissipative mode becomes non-dissipative, while for the high dissipative mode the damping coefficient becomes as twice as high as the damping coefficient of the system. A special element with controllable negative stiffness is suggested for designing hybrid materials whose stiffness and hence the dynamic behaviour is controlled by the magnitude of applied compressive force.     

Transitional regimes of penetrative convection in a plain layer

Penetrative convection in a plain layer of water is considered for the interval of temperatures containing the point of density maximum. When the unstable and stable layers are equal in the static conductive state, the development of convective instability is investigated from the formation of steady structures to chaotic motion. Scales of the periodicity cell for regimes with a strong nonlinear effect were chosen with particular attention. Specifics are shown for steady structures with small-scale vortices near upper boundaries and for periodic motions with synchronized oscillations of the lower parts of vertically elongated profiles of temperature that move symmetrically. With the increase of supercriticality, the motion loses reflection symmetry, becomes doubly periodic, and finally becomes quasi-periodic before transition to chaotic motion. Domains of hysteresis are investigated for which motions with different structure and heat fluxes coexist, and it is illustrated by the dependence of the Nusselt number on supercriticallity.     

基础水平运动的弹簧摆的周期解与稳定性

针对基础水平运动的弹簧摆的非线性动力学响应进行研究,利用拉格朗日方程建立了系统的动力学方程.将离散傅里叶变换、谐波平衡法以及同伦延拓方法相结合,对系统的周期响应进行求解,避免了传统方法计算中使用泰勒展开引起的小振幅的限制,与数值计算结果的对比表明该求解方法具有较高的精确度.利用Floquet理论分析了周期响应的稳定性,给出了基础运动振幅和频率对系统周期响应的影响.研究发现:对应某些基础频率和振幅,系统的周期响应可能发生Hopf分岔;利用数值计算研究了Hopf分岔后系统响应随基础频率和振幅的变化,发现系统出现了倍周期运动、拟周期运动和混沌等复杂的动力学行为.研究表明系统进入混沌的主要路径是拟周期环面破裂和阵发性.