MHD Flow and Heat Transfer of a Generalized Burgers' Fluid due to a Periodic Oscillating and Periodic Heating Plate

This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers' fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The momentum equation is formulated with multi-term fractional derivatives, and by means of viscous dissipation, the fractional derivative is considered in the energy equation. A finite difference scheme is established based on the G1-algorithm, whose convergence is confirmed by the comparison with the analytical solution in an example. Meanwhile the numerical solutions of velocity, temperature and shear stress are obtained. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Increasing the fractional derivative parameter α, the velocity and temperature have a decreasing trend, while the influences of fractional derivative parameter β on the velocity and temperature behave conversely. Increasing the absolute value of the first order slip parameter and the second order slip parameter both cause a decrease of velocity. Furthermore, with the decreasing of the magnetic parameter, the shear stress decreases.     

Effect of elasticity mismatch on cell deformation and migration:A phase-field study

The phase-field model for cell migration is used to study the effect of elasticity mismatch on the migration dynamics of multiple cells in a confluent monolayer, where one tagged cell is embedded by a number of normal cells and both types of cells are supposed to have the same properties except elasticity. Our results show that a larger elasticity mismatch leads to a larger difference in shape change between the tagged cell and the normal cells. We find that the bursts of velocity always fall behind the peak of the perimeter, and the shape change of the tagged cell results in the accelerated motion of the tagged cell in the whole process. Moreover, the variation of the averaging cell perimeter ratio ˉLtag/ˉLnormalwith the increase of the elasticity ratio γtag/γnormal for different active velocities |a| is analyzed. We find thatˉLtag/ˉLnormaldecreases with the increase of γtag/γnormal, following a simple power law function. Our results highlight the important role played by the cell elasticity mismatch in cell deformation and migration.     

Controlling the motion of solitons in BEC by a weakly periodic potential

By developing multiple-scale method combined with Wentzel--Kramer--Brillouin expansion, this paper analytically studies the modulating effect of weakly periodic potential on the dynamical properties of the Bose--Einstein condensates (BEC) trapped in harmonic magnetic traps. A black--grey soliton transition is observed in the BEC trapped in harmonic magnetic potential, due to the weakly periodic potential modulating effect. Meanwhile, it finds that with the slight increase of the weakly periodic potential strength, the velocity of the soliton decreases, while its width firstly decreases then increases, a minimum exists there. These results show that the amplitude, velocity, and width of matter solitons can be effectively managed by means of a weakly periodic potential.     

Resonant tunneling and quantum fluctuation in a driven triple-well system

The influence of parameters such as the strength and frequency of a periodic driving force on the tunneling dynamics is investigated in a symmetric triple-well potential. It is shown that for some special values of the parameters, tunneling could be enhanced considerably or suppressed completely. Quantum fluctuation during the tunneling is discussed as well and the numerical results are presented and analysed by virtue of Floquet formalism.     

Stochastic Resonance in a Coupled Array Without Periodic Driving

We manifest a stochastic resonance in a two-dimensional square array of coupled oscillators subjected only to white noise and constant driving forces.The result shows that the coherent output of every single oscillator plays the role of periodic input to its neighbours.Even without periodic driving,the cooperation of the white noise and the coupling can also result in the array enhanced stochastic resonance effect.In our investigation,global as well as local noise perturbation is taken into account.     

Stability of GOY Model Under Modulation of Periodic External Force

There is a phase transition between quasi-periodic state and intermittent chaos in GOY model with a critical value δ0. When we add a modulated periodic externa/force to the system, the phase transition can also be found with a critical value δe. Due to coupling between the force and the intrinsic fluctuation of the velocity on shells in GOY model, the stability of the system has been changed, which results in the variation of the critical value. For proper intensity and period of the force, δe is unequal to δ0. The critical value is a nonlinear function of amplitude of the force, and the fluctuation of the velocity can resonate with the external force for certain period Te.     

Frequency Response of Near-Wall Coherent Structures to Localized Periodic Blowing and Suction in Turbulent Boundary Layer

We experimentally investigate the frequency response of near-wall coherent structures to localized periodic blow- ing and suction through a spanwise slot in a turbulent boundary layer by changing the frequency of periodic disturbance at similar velocities of free stream. The effects of blowing and suction disturbance on energy redistri- bution, turbulent intensity U^＋ rums over y^＋ and waveforms of phase-averaged velocity during sweeping process are respectively discussed under three frequencies of periodic blowing and suction in near-wall region of turbulent boundary layer, compared with those in a standard turbulent boundary layer. The most effective disturbance frequency is figured out in this system.     

Mode-Locking Behaviour in Driven Colloids with Random Pinning

We find mode-locking steps in simulated force-velocity characteristics of external alternating-force （AF） driven colloids on a disordered substrate. Studies of mode-locking patterns in systems show that mode-locking steps are accompanied with the emergence of a dynamics phase： transverse solid phase. We also study the influence of temperature on the width of mode-locking steps. The mode-locked state is destroyed by thermal fluctuation and the width of mode-locking steps decreases rapidly with increasing temperature. In high velocity and low temperature regimes, due to the appearance of transverse solid phase and microscopically periodic velocity modulation, the step width changes little as temperature is varied.     

Active control of wall-bounded turbulence for drag reduction with piezoelectric oscillators

An experimental investigation was performed for active control of coherent structure bursting in the near-wall region of the turbulent boundary layer. By means of synchronous and asynchronous vibrations with double piezoelectric vibrators,the influence of periodic vibration of the double piezoelectric vibrators on the mean velocity profile, drag reduction rate, and coherent structure bursting is analyzed at Re_θ= 2766. The case with 100 V/160 Hz-ASYN is superior to other conditions in the experiment and a relative drag reduction rate of 18.54% is exciting. Asynchronous vibration is more effective than synchronous vibration in drag reduction at the same voltage and frequency. In all controlled cases, coherent structures at large scales are regulated while the small-scale structures are stimulated. The fluctuating velocity increases significantly. A periodic regulating effect on the coherent structure can be seen in the ASYN control conditions at the frequency of 160 Hz.     

Pressure Oscillating Flow in Corrugated Parallel Channel

The approximate analytical solution of velocity is presented for incompressible and viscous fluid driven by the oscillation of the periodic pressure, between two slit parallel plates with corrugated walls by employing perturbation method. The corrugations of the two walls are described as periodic sinusoidal waves with small amplitude either in phase or half-period out of phase. Based on the analysis, we discuss the influence of the dimensionless parameters on velocity u±and mean velocity parameter φ±numerically, such as Reynolds number Re, nondimensional amplitude A of pressure gradient and wave number k.     

二维耦合定向输运模型研究

建立了外部驱动力及噪声作用下的二维耦合定向输运模型, 其中的一个维度上为周期性分段棘齿势, 另一垂直维度上为周期性对称非棘齿势, 外部驱动力及噪声加在周期对称非棘齿势方向上, 而棘齿势方向不加任何驱动, 采用非平衡统计及非线性动力学理论研究了过阻尼情况下耦合系统在两个维度上的输运性质. 结果显示, 棘齿势与非棘齿势方向均可产生定向输运, 其中棘齿势方向的系统平均速度对耦合强度、噪声强度、驱动力强度及粒子数目均有明显的依赖性, 合适的耦合强度、噪声强度、驱动力强度或粒子数目下均可产生最大输运速度. 而非棘齿势方向的系统平均速度受非棘齿势势垒高度影响显著, 但随耦合强度、驱动力强度、驱动力初相位差及粒子数目的变化均出现波动现象, 表现出平均速度对这些参量的依赖性较弱.     

Directed Current Induced by an Symmetrically ac Force Coexisting with a Time-Delayed Feedback

We study the transport of overdamped Brownian particles in a symmetrically periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback.It is found that for low frequencies,the average velocity can be negative by changing the driving amplitude,for high frequencies,there exists an optimized driving amplitude at which the average velocity takes its maximum value.Additionally,there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies.For the large value of the delay time,the average velocity is independent of the delay time.     

Self-healing slip pulses along a gel/glass interface

We present experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity: steady sliding at high velocity (>V(c) approximately 100--125 microm/s), characterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a "healing instability" occurring when the local sliding velocity reaches the macroscopic transition velocity V(c). At driving velocities close below V(c), the system exhibits complex spatiotemporal behavior.     

Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases,stability phase diagram and collapse dynamics

We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose−Einstein condensates (BECs) with tunable spin−orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross−Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.     

Nonlinear Dynamics of a Sliding Chain in a Periodic Potential

Nonlinear dynamics of the sliding process of a chain driven with a constant velocity at one end in a periodic substrate potential is investigated. The driven chain exhibits distinctly different dynamical characteristics at different velocities. In the low velocity region, the chain moves in a stick-slip manner. When the driving velocity is increased, the stick-slip behaviour is replaced by complicated and regular oscillatory motions. The dependence of the dynamics on the coupling strength is studied and the step-like behaviour is found, where different steps correspond to different dynamical phases.     

A dynamical transition of a chain of charged particles in a 2D substrate potential

The transport of a chain of charged particles with a transverse degree of freedom is investigated in a 2D asymmetric potential. Here, the energy of the periodic driving force is converted into motion in the vertical direction. The analysis exhibits a transition from stick-slip motion to periodic oscillation. The chain velocity can be controlled to an optimized value by adjusting system parameters, such as the amplitude and frequency of the periodic force. The existence of a resonance platform indicates resonance between the motion of the chain and the periodic force as coupling strength increases adiabatically. The atomic configuration and the transverse degree of freedom also play key roles in the control.     

Directional Mode-Locking of Dynamics of Two-Dimensional Superparamagnetic Colloidal System in a Periodic Pinning Array

Using Langevin simulations,we study numerically the directional mode-locking of the dynamics of twodimensional superparamagnetic colloidal system in a periodic pinning array.When the colloidal particles are initially commensurate with the pinning sites,there appear mode-locking steps in the average velocity of colloidal particles along certain directions of the external driving force.With an increase in the pinning strength,the width of the step increases linearly but the velocity at the step decreases parabolically.     

Static friction on the fly: velocity depinning transitions of lubricants in motion

The dragging velocity of a model solid lubricant confined between sliding periodic substrates exhibits a phase transition between two regimes, respectively, with quantized and with continuous lubricant center-of-mass velocity. The transition, occurring for increasing external driving force F ext acting on the lubricant, displays a large hysteresis, and has the features of depinning transitions in static friction, only taking place on the fly. Although different in nature, this phenomenon appears isomorphic to a static Aubry depinning transition in a Frenkel-Kontorova model, the role of particles now taken by the moving kinks of the lubricant-substrate interface. We suggest a possible realization in 2D optical lattice experiments.     

相位差法测受迫振动的阻尼系数

利用音叉在受迫阻尼振动中速度与驱动力之间的相位差测定了阻尼系数.该方法在系统的稳定状态下读数,克服了通常所用的振幅衰减方法中的不稳定性,可降低人为因素给测量带来的误差.