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.     

Denaturation transition of stretched DNA

We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent c, for which we find the new value c = 4 nu-1/2 such that the transition is second order with c = 1.85 < 2 in d = 3. We show that a finite stretching force F destabilizes DNA, corresponding to a lower melting temperature T(F), in agreement with single-molecule DNA stretching experiments.     

Quantum depinning transition of quantum Hall stripes

We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor Deltanu(c). For DeltanuDeltanu(c). For Deltanu> or =Deltanu(c), we find a partial RSB solution in which there is free sliding only along the stripe direction. The transition is analogous to the Kosterlitz-Thouless phase transition.     

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.     

Critical dynamics associated with dynamic disordering near the depinning transition in different vortex phases

We study a depinning transition based on transient dynamics of vortices driven by a suddenly applied dc current, focusing on whether a difference in the equilibrium vortex phase that can lead to a different vortex flow will change the critical behavior. After preparing an ordered initial vortex configuration, we measure the time evolution of voltage associated with dynamic disordering in three magnetic fields, corresponding to the ordered phase (OP), disordered phase (DP), and coexistence phase. The critical behavior of the depinning transition is commonly observed in these phases, pointing to the universality of the transition. However, the critical behavior is most marked in the coexistence phase, while the suppression of the critical region and that of dynamic disordering are observed in OP and DP, respectively, whose origin is attributed to the different flow states among these phases.     

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.     

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.     

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.     

Depinning transition of the quenched Mullins-Herring equation: A short-time dynamic method

The depinning phase transition of the Mullins-Herring equation with an external driving force and quenched random noise is studied in a short-time dynamic scaling scheme. Besides the critical driving force, all the critical exponents can be accessed, agreeing well with those in long-time steady-state simulations. The finite size effects on the critical exponents are also discussed. It is found that reasonable results can be achieved with a relatively small system, which highlights the advantage of the present approach.     

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.     

Metastability and uniqueness of vortex states at depinning

We present results from numerical simulations of the transport of vortices in the zero-field-cooled (ZFC) and the field-cooled (FC) state of a type-II superconductor. In the absence of an applied current I, we find that the FC state has a lower defect density than the ZFC state, and is stable against thermal cycling. On the other hand, by cycling I, surprisingly, we find that the ZFC state is the stable state. The FC state is metastable as manifested by increasing I to the depinning current I(c), in which case the FC state evolves into the ZFC state. We also find that all configurations acquire a unique defect density at the depinning transition independent of the history of the initial states.     

Bell's expression and the generalized Garg form for forced dissociation of a biomolecular complex

The dissociation of a biomolecular complex under the action of constant force, constant loading rate, and periodic force is studied theoretically. We show that the celebrated Bell expression provides a good approximation for the bond dissociation rate when F/F(c)<1, where F(c) is the maxima slope of the binding potential along the reaction coordinate. When 1-F/F(c) <1 the dissociation rate is better described by a generalized Garg form in which the potential derivative is expanded near F(c). We also show that a constant-force experiment is suitable for extracting the activation energy of the bond, a constant loading experiment is suitable to extract F(c), while time-periodic force can be applied to extract both bond dissociation rates at zero force and F(c).     

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.     

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.     

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.     

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.     

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.     

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.     

Force network ensemble: a new approach to static granular matter

An ensemble approach for force distributions in static granular packings is developed. This framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. We show how the formalism yields realistic results, both for disordered and regular triangular "snooker ball" configurations, and obtain a shear-induced unjamming transition of the type proposed recently for athermal media.