Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dlmensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling fit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic depinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Depinning dynamics of driven colloids with random pinning： a numerical study

Using Langevin simulations, we have investigated numerically the depinning dynamics of driven two-dimensional colloids subject to the randomly distributed point-like pinning centres. With increasing strength of pinning, we find a crossover from elastic to plastic depinnings, accompanied by an order to disorder transition of state and a substantial increase in the depinning force. In the elastic regime, no peaks are found in the differential curves of the velocity－force dependence (VFD) and the transverse motion is almost none. In addition, the scaling relationship between velocity and force is found to be valid above depinning. However, when one enters the plastic regime, a peak appears in the differential curves of VFD and transverse diffusion occurs above depinning. Furthermore, history dependence is found in the plastic regime.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dimensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling lit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic de. Pinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

受驱无序胶体动力学

利用Langevin分子动力学，本数值研究点钉扎中心随机分布的二维胶体动力学．随着钉扎中心强度的提高，我们发现了从弹性脱钉到塑性脱钉的渡越，并伴随临界钉扎力在渡越区的明显提高，类似于超导体中的峰值效应．另外，我们首次发现：当塑性流动发生时，高速运动胶体粒子感受到的平均钉扎力在从玻璃态到液态的转变过程中会出现峰值效应，并伴随有速度-驱动力曲线的交叠．     

Depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers

We study, by Langevin simulations, the depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers. When the number ratios of pinnings to colloids are 1:1 matching and at finite temperature, we find for the first time crossovers from plastic flow through elastic smectic flow to elastic crystal flow near the depinning with increasing the pinning strength. There exists a power-law scaling relationship between the average velocity of colloids and the external driving force for all the three types of flows. It is found that the critical driving force and the power-law scaling exponent as well as the average intensity of Bragg peaks are invariant basically in the region of elastic smectic flow. We also examine the temperature effect and it reveals that the above dynamic moving phases and their transitions could be attributed to the interplay between thermal fluctuation and pinning potential. At sufficiently low temperature, the thermal fluctuation could be neglected and the colloids near the depinning move in the elastic crystal flow no matter what the pinning strength. In addition, the number of pinning centers is changed and when it is close to the number of colloids, there appears a peak in the critical driving force and a dip in the power-law scaling exponent, respectively. The peak and dip are more pronounced for higher pinning strength.     

Nonuniversality of Critical Exponents in a Fractional Quenched Kardar–Parisi–Zhang Equation

In this article we address the problem of the depinning transition for driven interfaces in random media. We introduce a fractional Kardar–Parisi–Zhang equation with quenched noise, in which the normal diffusion term is replaced by a fractional Laplacian accounting for long-range interactions through quenched disorder. The critical values of the external driving force and nonlinear term coefficient evidently depend on the system size at the depinning transition. For a fixed value of the external driving force, the fractional order much determines the value of the nonlinear term coefficient that leads to a depinned interface. Near the depinning threshold, the critical exponent obtained numerically is nonuniversal, and weakly depends on the fractional order.     

Depinning Dynamics of Two-Dimensional Charged Colloids on a Random Laser-Optical Substrate

Using Langevin simulations, we. investigate the depinning dynamics of two-dimensional charged colloids on a random laser-optical substrate. With an increase in the strength of the substrate, we find a transition from crystal to smectic flows above the depinning. A power-law scaling relationship between average velocity and applied driving force could be obtained for both flows, and we find that the scaling exponents are no bigger than 1 for the crystal and are bigger than 1 for the smectic flows.     

Nonlinear mobility of a driven system: Temperature and disorder effects

We consider the dissipative nonlinear dynamics of a model of interacting atoms driven over a substrate potential. The substrate parameters can be suitably tuned in order to introduce disorder effects starting from two geometrically opposed ideal cases: commensurate and incommensurate interfaces. The role of temperature is also investigated through the inclusion of a stochastic force via a Langevin molecular dynamics approach. Here, we focus on the most interesting tribological case of underdamped sliding dynamics. For different values of the chain stiffness, we evaluate the static friction threshold and consider the depinning transition mechanisms as a function of the applied driving force. As experimentally observed in QCM frictional measurements of adsorbed layers, we find that disorder operates differently depending on the starting geometrical configuration. For commensurate interfaces, randomness lowers considerably the chain depinning threshold. On the contrary, for incommensurate mating contacts, disorder favors static pinning destroying the possible frictionless (superlubric) sliding states. Interestingly, thermal and disorder effects strongly influence also the occurrence of parametric resonances inside the chain, capable of converting the kinetic energy of the center-of-mass motion into internal vibrational excitations. We comment on the nature of the different dynamical states and hysteresis (due to system bi-stability) observed at different increasing and decreasing strengths of the external force.     

Depinning Dynamics of Fluid Monolayer on a Quenched Substrate

Langevin simulations are preformed on the depinning dynamics of fluidmonolayer on a quenched substrate. With increase in the strength of thesubstrate, we find for the first time a crossover from elastic crystal tosmectic flows as well as a crossover from smectic to plastic flows above thedepinning. A power-law scaling relationship can be derived between the driftvelocity and the driving force for both the elastic crystal and smecticflows, but fails to be obtained for the plastic flow. The power-lawexponents are found to be no larger than 1 for the elastic crystal flow andlarger than 1 for the smectic flow. The critical driving force and theaveraged intensity of Bragg peaks remain invariant basically in the regimeof smectic flow. A sudden increase in the critical driving force is observedwithin the crossover from the smectic to plastic flows, and the averagedintensity of Bragg peaks shows sudden decreases within the crossovers bothfrom the elastic crystal to smectic flows and from the smectic to plastic flows.The results are helpful for understanding the slip dynamics of fluids on a molecular level.     

Peak Effect and the Phase Diagram of Moving Vortices in FexNi1-xZr2 Superconducting Glasses

In the mixed state of type II superconductors, vortices penetrate the sample and form a correlated system due to the screening of supercurrents around them. Interestingly, we can study this correlated system as a function of density and driving force. The density, for instance, is controlled by the magnetic field B, whereas a current density j acts as a driving force F=j x B on all vortices. To minimize the pinning strength, we study a superconducting glass in which the depinning current is 10 to 1000 times smaller than in previous studies, which enables us to map out the complete phase diagram in this new regime. The diagram is obtained as a function of B, driving current, and temperature, and leads to a remarkable set of new results, which includes a huge peak effect, an additional reentrant depinning phase, and a driving force induced pinning phase.     

Driven quasi-one-dimensional classical electron gas in the presence of a constriction: Pinning and depinning

We studied the properties of a quasi-one-dimensional system of charged particles in the presence of a local Lorentzian-shaped constriction. We investigated the response of the system when a time-independent external driving force is applied in the unconfined direction. Langevin molecular dynamics simulations for different values of the drive and temperature are performed. We found that the particles are pinned unless a threshold value of the driving force is reached. We investigated in detail the depinning phenomenon. The system can depin “elastically”, with particles moving together and keeping their neighbors, or “quasi-elastically”, with particles moving together through a complex net of conducting channels without keeping their neighbors. In the case of elastic depinning the velocity vs applied drive curves is characterized by a critical exponent β consistent with the value , while in the case of quasi-elastic depinning the critical exponent β has on average the value 0.94. The model is relevant e.g. for electrons on liquid helium, colloids and dusty plasma.     

Moving Wigner glasses and smectics: dynamics of disordered Wigner crystals

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conduction noise and I(V) curves. For strong disorder, we show criticality in the voltage onset just above depinning. We obtain the dynamic phase diagram for driven Wigner solids and demonstrate a finite threshold of force for transverse sliding, recently observed experimentally.     

Dynamics below the depinning threshold in disordered elastic systems

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T-->0, the steady state is dominated by a single configuration which is occupied with probability 1. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady-state regime as the depinning threshold is approached from below. We do find a divergent length, but it is associated only with the transient relaxation between metastable states.     

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments. Received: 13 February 1998 / Accepted: 30 March 1998     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Transport in a ratchet with spatial disorder and time-delayed feedback

A Brownian motor with Gaussian short-range correlated spatial disorder and time-delayed feedback is investigated. The effects of disorder intensity, correlation strength and delay time on the transport properties of an overdamped periodic ratchet are discussed for different driving force. For small driving force, the disorder intensity can induce a peak in the drift motion and a linear increasing function in diffusion motion. For large driving force, the disorder intensity can suppress the drift motion but enhance the diffusion motion. For both small and large driving forces, the correlation strength of the spatial disorder can enhance the drift motion but suppress the diffusion motion. While the delay time can reduce the drift motion to a small value and enhance the diffusion motion to a large value. The drift motion increases as the driving force increases. However, the diffusion motion is either decreases or only increases slightly when the driving force increases.     

Depinning and creep motion in glass States of flux lines

Using dynamical computer simulation, we investigate vortex matter in glass states. A genuine continuous depinning transition is observed at zero temperature, which also governs the low-temperature creep motion. With the notion of scaling, we evaluate in high accuracy critical exponents and scaling functions; we observe a non-Arrhenius creep motion for weak collective pinning where the Bragg glass is stabilized at equilibrium, while for strong pinning, the well-known Arrhenius law is recovered. In both cases, a sharp crossover takes place between depinning and creep at low temperatures.     

Dynamics of vortices in type-II superconductors with periodic square columnar pins

The dynamics of a two-dimensional vortex system with strong periodic square columnar pins is investigated. For the case vortex number matching pinning number, we find that the vortex liquid is frozen into square lattice via a continuous transition, and the freezing (melting) temperature T_m is the same as the thermal depinning temperature of vortices, which are different from the first-order phase transition at weak pinning. The zero-temperature critical depinning force F_c0 is exactly the same as the maximum pinning force, and the depinning property at T = 0 can be expressed by scaling v ～ (F ? F_c0)^β with the exponent β close to 0.5. The v–F curves at temperatures below T_m show that vortices are pinned at small driving force.     

Renormalization of pinned elastic systems: how does it work beyond one loop?

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find zeta = epsilon/3(1 + 0.143 31 epsilon), epsilon = 4 - d, in violation of the conjecture zeta = epsilon/3, solving the discrepancy with simulations. For long range elasticity zeta = epsilon/3(1 + 0.397 35 epsilon), epsilon = 2 - d, much closer to the experimental value (approximately 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.     

Simulation of Dynamics in Two-Dimensional Vortex Systems in Random Media

Dynamics in two-dimensional vortex systems with random pinning centres is investigated using molecular dynamical simulations. The driving force and temperature dependences of vortex velocity are investigated. Below the critical depinning force Fc, a creep motion of vortex is found at low temperature. At forces slightly above Fc, a part of vortices flow in winding channels at zero temperature. In the vortex channel flow region, we observe the abnormal behaviour of vortex dynamics： the velocity is roughly independent of temperature or even decreases with temperature at low temperatures. A phase diagram that describes different dynamics of vortices is presented.