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.     

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.     

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.     

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．     

On the dynamics of sliding elastic manifolds with random interaction

The friction dynamics of contacting D-dimensional disordered elastic manifolds, driven by external forces, is studied, and the existence of a zero-temperature depinning transition below some critical dimensionality is demonstrated for different kinds of elastic response. It is shown that this model falls into the universality class of single interface depinning in a 2D-dimensional random medium. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 532–537 (25 October 1996) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

Universal statistics of the critical depinning force of elastic systems in random media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.     

Structural depinning of Ne monolayers on Pb at T < 6/5 K

We have studied the nanofriction of Ne monolayers with a quartz-crystal microbalance technique at temperatures below 6.5 K and in ultrahigh-vacuum conditions. Very homogeneous and smooth lead electrodes have been physically deposited on a quartz blank at 150 K and then annealed at room temperatures. With such a Pb-plated quartz-crystal microbalance, we have observed a pronounced depinning transition separating a low-coverage region, where the film is nearly locked to the oscillating electrode, from a high-coverage region characterized by slippage at the solid-fluid boundary. Such a behavior has been found to be very reproducible. These data are suggestive of a structural depinning of the solid Ne film when it becomes incommensurate with the lead substrate, in agreement with the results of an extensive molecular-dynamics study.     

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.     

Can nonlinear elasticity explain contact-line roughness at depinning?

We examine whether cubic nonlinearities, allowed by symmetry in the elastic energy of a contact line, may result in a different universality class at depinning. Standard linear elasticity predicts a roughness exponent zeta = 1/3 (one loop), zeta = 0.388 +/- 0.002 (numerics) while experiments give zeta approximately = 0.5. Within functional renormalization group methods we find that a nonlocal Kardar-Parisi-Zhang-type term is generated at depinning and grows under coarse graining. A fixed point with zeta approximately = 0.45 (one loop) is identified, showing that large enough cubic terms increase the roughness. This fixed point is unstable, revealing a rough strong-coupling phase. Experimental study of contact angles theta near pi/2, where cubic terms in the energy vanish, is suggested.     

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.     

Depinning with dynamic stress overshoots: mean field theory

An infinite-range model of an elastic manifold pulled through a random potential by a force F is analyzed focusing on inertial effects. When the inertial parameter M is small, there is a continuous depinning transition from a small- F static phase to a large- F moving phase. When M is increased to M(c), a novel tricritical point occurs. For M>M(c), the depinning transition becomes discontinuous with hysteresis. Yet, the distribution of discrete "avalanche"-like events as the force is increased in the static phase for M>M(c) has an unusual mixture of first-order-like and critical features. The results may be relevant for the onset of crack propagation and for dynamics of geological faults.     

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.     

Elastic properties of nanostructured materials with layered grain boundary structure

Atomistic calculations of the elastic constants for a bulk nanostructured material that consists of a layered structure where alternating layers meet along high angle grain boundaries and where atoms interact via a Lennard-Jones potential are presented. The calculations of the elastic constants were performed in the frame of homogeneous deformations for a wide range of layer widths ranging from 2.24 up to 74.62 nm. The results showed that the relaxation of the atomic structure affects the elastic constants for the cases where more than 5% of atoms are located in the GB region. Also it was found that the way that external stresses are applied on the system affects the values of the obtained elastic properties, with the elastic constants related to the characteristic directions of the grain boundary being the most affected ones. The findings of this work are of interest for the fabrication methods of nanostructured materials, the measurement methods of their elastic properties as well as multiscale modeling schemes of nanostructured materials.     

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.     

Renormalisation group for depinning transition ind=2 ising models

We develop a position space renormalisation group (RG) method to study generalised depinning transition in two-dimensional Ising models. The treatment encompasses (i) the original model for depinning invented by Abraham, (ii) generalised depinning model, (iii) nonuniversal behaviour near the internal line of defects and (iv) surface and interface behaviour. The phase diagrams and the thermodynamic functions over the whole range of temperatures are obtained. The agreement with exact results (when available) is quite satisfactory.     

Universal magnetic domain wall dynamics in the presence of weak disorder

The motion of elastic interfaces in disordered media is a broad topic relevant to many branches of physics. Field-driven magnetic domain wall motion in ultrathin ferromagnetic Pt/Co/Pt films can be well interpreted within the framework of theories developed to describe elastic interface dynamics in the presence of weak disorder. Indeed, the three theoretically predicted dynamic regimes of creep, depinning, and flow have all been directly evidenced in this model experimental system. We discuss these dynamic regimes and demonstrate how field-driven creep can be controlled not only by temperature and pinning, but also via interactions with magnetic entities located inside or outside the magnetic layer. Consequences of confinement effects in nano-devices are briefly reviewed, as some recent results on domain wall motion driven by an electric current or assisted by an electric field. Finally new theoretical developments and perspectives are discussed.     

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