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.     

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.     

Colloidal dynamics on disordered substrates

Using Langevin simulations, we examine driven colloids interacting with quenched disorder. For weak substrates the colloids form an ordered state and depin elastically. For increasing substrate strength, we find a sharp crossover to inhomogeneous depinning and a substantial increase in the depinning force, analogous to the peak effect in superconductors. The velocity versus driving force curve shows criticality at depinning, with a change in scaling exponent occurring at the order to disorder crossover. Upon application of a sudden pulse of driving force, pronounced transients appear in the disordered regime which are due to the formation of long-lived colloidal flow channels.     

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.     

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.     

Plastic flow in a driven random-field XY model

Plastic depinning and flow in a one-dimensional random-field XY model in the presence of a driving force are investigated numerically. From the analysis of velocity-force and related characteristics, it is found that a scaling relation holds in plastic flow states under strong pinning conditions.     

Models of plastic depinning of driven disordered systems

Two classes of models of driven disordered systems that exhibit historydependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.     

Viscoelastic depinning of driven systems: mean-field plastic scallops

We have investigated the mean-field dynamics of an overdamped viscoelastic medium driven through quenched disorder. The model allows for the coexistence of pinned and sliding regions and can exhibit continuous elastic depinning or first-order hysteretic depinning. Numerical simulations indicate mean-field instabilities that correspond to macroscopic stick-slip events and lead to premature switching. The model describes the elastic and plastic dynamics of driven vortex arrays in superconductors and other extended disordered systems.     

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．     

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.     

A Solvable Model of Interface Depinning in Random Media

We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written directly for an infinite system. For a flat distribution of random local forces the value of the depinning threshold can be obtained exactly. In the case of parallel dynamics (all unstable sites move simultaneously), due to the discrete character of the interface heights allowed in the model, the motion of the center of mass is non-uniform in time in the moving phase close to the threshold, and the mean interface velocity vanishes with a square-root singularity.     

NUMERICAL STUDIES ON THE DYNAMICS OF DISORDERED VORTEX LATTICE

Flow behavior of the driven two-dimensional vortex lattice is numerically studied with different densities of randomly distributed pointlike pinning centers. Different features in the curves of velocity-force dependence are found between the elastic and plastic regimes. Scaling fit between force and velocity above the critical driving force can be obtained in the elastic regime but fails in the plastic regime. Transition from the lastic to plastic regimes is accompanied by maximum peaks in the differential curves of velocity-force dependence in the disordered vortex lattice.     

Interface Motion in Disordered Ferromagnets

We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by logarithmic corrections. This suggests that d = 5 is the upper critical dimension of the depinning transition in the random-field Ising model. Furthermore, we investigate the so-called creep regime (small driving fields and temperatures) where the interface velocity is given by an Arrhenius law.     

From weak to strong pinning I: A finite size study

We have used linear stability analysis to study the depinning of an elastic chain with long range interactions submitted to a random pinning potential. In this paper, we provide, for the first time, evidence of a pronounced change from a strong pinning regime to a weak pinning regime. This change depends on the strength of disorder, and takes place only in finite size systems. For a given disorder, we show a characteristic length separating the weak pinning regime from the strong pinning regime. This length depends on the long range of the algebraic decay of the elastic couplings. The weak pinning regime is very well described by perturbation theory. As an example, we discuss more specifically the case of wetting of heterogeneous surfaces, where the change from a strong to a weak pinning regime could be induced in the wetting front by varying the surface tension of the liquid-air interface.Received: 12 September 2003, Published online: 20 April 2004PACS: 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 68.08.Bc Wetting - 02.50.Fz Stochastic analysis     

Dynamic critical phenomena in two-dimensional fully frustrated Coulomb gas model with disorder

The dynamic critical phenomena near depinning transition in two-dimensional fully frustrated square lattice Coulomb gas model with disorders was studied using Monte Carlo technique. The ground state of the model system with disorder σ=0.3 is a disordered state. The dependence of charge current density J on electric field E was investigated at low temperatures. The nonlinear J-E behavior near critical depinning field can be described by a scaling function proposed for three-dimensional flux line system [M.B. Luo, X. Hu, Phys. Rev. Lett. 98 (2007) 267002]. We evaluated critical exponents and found an Arrhenius creep motion for field region Ec/2<E<Ec. The scaling law of the depinning transition is also obtained from the scaling function.     

Domain wall depinning in random media by ac fields

The viscous motion of an interface driven by an ac external field of frequency omega(0) in a random medium is considered here in the nonadiabatic regime. The velocity exhibits a smeared depinning transition showing a double hysteresis which is absent in the adiabatic case omega(0)-->0. Using scaling arguments and an approximate renormalization group calculation we explain the main characteristics of the hysteresis loop. In the low frequency limit these can be expressed in terms of the depinning threshold and the critical exponents of the adiabatic case.     

Dynamics of two-dimensional vortex system in a strong square pinning array at the second matching field

We study the dynamics of a two-dimensional vortex system in a strong square pinning array at the second matching field. Two kinds of depinning behaviors, a continuous depinning transition at weak pinning and a discontinuous one at strong pinning, are found. We show that the two different kinds of vortex depinning transitions can be identified in transport as a function of the pinning strength and temperature. Moreover, interstitial vortex state can be probed from the transport properties of vortices.     

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