Self-synchronization of coupled oscillators with hysteretic responses

We analyze a large system of nonlinear phase oscillators with sinusoidal nonlinearity, uniformly distributed natural frequencies and global all-to-all coupling, which is an extension of Kuramoto's model to second-order systems. For small coupling, the system evolves to an incoherent state with the phases of all the oscillators distributed uniformly. As the coupling is increased, the system exhibits a discontinuous transition to the coherently synchronized state at a pinning threshold.of the coupling strength, or to a partially synchronized oscillation coherent state at a certain threshold below the pinning threshold. If the coupling is decreased from a strong coupling with all the oscillators synchronized coherently, this coherence can persist until the depinning threshold which is less than the pinning threshold, resulting in hysteretic synchrony depending on the initial configuration of the oscillators. We obtain analytically both the pinning and depinning threshold and also expalin the discontinuous transition at the thresholds for the underdamped case in the large system size limit. Numerical exploration shows the oscillatory partially coherent state bifurcates at the depinning threshold and also suggests that this state persists independent of the system size. The system studied here provides a simple model for collective behaviour in damped driven high-dimensional Hamiltonian systems which can explain the synchronous firing of certain fireflies or neural oscillators with frequency adaptation and may also be applicable to interconnected power systems.     

Dynamics and hysteresis of the contact line between liquid hydrogen and cesium substrates

We have measured both the hysteresis and the dynamics of the edge of a liquid hydrogen meniscus on several solid cesium substrates. We find that the dynamics of the contact line is thermally activated. For all substrates, we find that the activation energy is of the order of the hysteresis. We show that the pinning of the contact line on mesoscopic defects of the Cs substrate is likely to control both the hysteresis and the dynamics of the contact line at low velocity, close to the depinning threshold. Such a mechanism could be relevant also for simple room-temperature systems.     

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.     

Quantum mechanisms of density wave transport

We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe₃ and TaS₃, as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates.     

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.     

Domain wall motion in perpendicular anisotropy nanowires with edge roughness

We study field-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy using finite element micromagnetic simulations. Edge roughness is introduced by deforming the finite element mesh, and we vary the correlation length and magnitude of the roughness deformation separately. We observe the Walker breakdown both with and without roughness, with steady DW motion for applied fields below the critical Walker field H(c), and oscillatory motion for larger fields. The value of H(c) is not altered in the presence of roughness. The edge roughness introduces a depinning field. During the transient process of depinning, from the initial configuration to steady DW motion, the DW velocity is significantly reduced in comparison to that for a wire without roughness. The asymptotic DW velocity, on the other hand, is virtually unaffected by the roughness, even though the magnetization reacts to the edge distortions during the entire course of motion, both above and below the Walker breakdown. A moving DW can become pinned again at some later point ('dynamic pinning'). Dynamic pinning is a stochastic process and is observed both for small fields below H(c) and for fields of any strength above H(c). In the latter case, where the DW shows oscillatory motion and the magnetization in the DW rotates in the film plane, pinning can only occur at positions where the DW reverses direction and the instantaneous velocity is zero, i.e., at the beginning or in the middle of a positional oscillation cycle. In our simulations pinning was only observed at the beginnings of cycles, where the magnetization is pointing along the wire. The depinning field depends linearly on the magnitude of the edge roughness. The strongest pinning fields are observed for roughness correlation lengths that match the domain wall width.     

Charge density wave transport in NbSe<Subscript>3</Subscript> at low temperatures under high magnetic field

Charge density wave (CDW) depinning and sliding regimes have been studied in NbSe₃ at low temperatures down to 1.5 K under magnetic field of 19 T oriented along the c-axis. We found that the threshold field for CDW depinning becomes temperature independent below T ₀ ≈ 15 K. Also CDW current to frequency ratio characterizing CDW sliding regime increases by factor 1.7 below this temperature. The results are discussed as a crossover from thermal fluctuation to tunneling CDW depinning at T < T ₀. Besides, we found that CDW sliding strongly suppresses the amplitude of Shubnikov-de Haas oscillations of magnetoresistance.     

Threshold field in nucleation process for an inhomogeneous deformable nonlinear Klein-Gordon system

We investigate the effect of local inhomogeneity on the nucleation process of kink-antikink pairs in the driven nonlinear Klein-Gordon model with the Remoissenet-Peyrard substrate potential, whose shape can be varied as a function of the shape parameter and which has the sine-Gordon shape as a particular case. From numerical integrations of the model equations under defined conditions, the configuration of the critical nucleus in the presence of a localized inhomogeneity is determined and shown to be affected by the shape parameter of the substrate potential. The expression of the depinning threshold field of kink-antikink pairs, which is the value of the applied field at which the process of the nucleation of kink-antikink pairs takes place, is also obtained. The dependence of this depinning threshold field on the shape parameter r shows that it strongly increases, for small intensity of the impurity potential when the shape of the substrate potential deviates from the sinusoidal one.     

Coupling between precipitation and contact-line dynamics: multiring stains and stick-slip motion

The contact line in an evaporating drop can stay pinned to form a single ring or can shrink in a discontinuous stepwise manner and generate multiple rings. We demonstrate the latter with DNA solutions and attribute it to a pinning-depinning cycle that generates new contact lines. The new contact line recedes after depinning and is repinned at an internal precipitate ring that determines the location of the next contact line. Each precursor ring is formed when DNAs are trapped by an internal microstagnation flow and precipitation dynamics hence control this unsteady drop motion.     

Depinning of a metastable disordered vortex lattice

We report on experiments investigating the depinning dynamics of a strongly pinned vortex lattice in 2H-NbSe2. We find that the depinning process starts at currents that are well below the critical current of the entire lattice and that it is governed by the formation of contiguous channels of mobile vortices connecting the sample edges. We obtain the formation time of the first channel by monitoring the delayed voltage response to a driving current step and by measuring the ramping rate dependence of the critical current. The subsequent increase in the number of moving vortices is determined from the temporal evolution of the voltage response and the critical current.     

Multi-scale analysis of the stress state in a granular slope in transition to failure

By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted toward its angle of repose. An increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, we introduce a coarse-graining length scale at which all stress ratios are below the packing yield threshold. We show that this length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the angle of repose. This transition coincides with the onset of dilation in the packing. We map this transition into a percolation transition of the overloaded grains, and discuss it in terms of long-range correlations and granular slope metastability.     

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.     

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.     

Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires

A magnetic domain wall (DW) injected and pinned at a notch in a permalloy nanowire is shown to exhibit four well-defined magnetic states, vortex and transverse, each with two chiralities. These states, imaged using magnetic force microscopy, are readily detected from their different resistance values arising from the anisotropic magnetoresistance effect. Whereas distinct depinning fields and critical depinning currents in the presence of magnetic fields are found, the critical depinning currents are surprisingly similar for all four DW states in low magnetic fields. We observe current-induced transformations between these DW states below the critical depinning current which may account for the similar depinning currents.     

Collective Cooper-pair transport in the insulating state of Josephson-junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson-junction arrays. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are nonmonotonic functions of the magnetic field. We propose that formation of the dynamic Coulomb barrier and its size scaling are consequences of the mutual Josephson phase synchronization across the system. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.     

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.     

Sliding-induced decoupling and charge transfer between the coexisting Q1 and Q2 charge density waves in NbSe3

Using high-resolution x-ray scattering in the presence of an applied current, we report evidence for a dynamical decoupling between the two NbSe3 charge-density waves (CDWs), Q1 (T(C1)=145 K) and Q2 (T(C2)=59 K), coexisting below T(C2). Simultaneous and oppositely directed shifts of the relevant CDW superlattice spots develop above a threshold current which we identify as the depinning threshold I(C1) for the more strongly pinned upper CDW Q1 (I(C1) approximately 10I(C2)). In contrast with shifts induced by current conversion processes, the present effect is not current polarized and is not limited to the current-contact regions. We propose a model which explains this instability through a sliding-induced charge transfer between the two electronic reservoirs corresponding to the Q1 and Q2 CDWs.     

The behavior of the critical current density below and above the first matching field in superconductors with periodic square arrays of pinning sites

We have studied the effect of the applied magnetic field on critical depinning force at zero and finite temperatures and for several values of pinning strength. This was achieved by conducting extensive series of molecular dynamic simulations on driven vortex lattices interacting with periodic square arrays of pinning sites. We have found that the critical depinning force decreases as the applied magnetic field is increased. We have also observed two distinct behaviors of dependence of the critical depinning force on the applied magnetic field below and above the first matching filed.     

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.     

Nonlinear conductivity and narrow band noise in NbSe3

A charge density wave system near commensurability and with strong damping is considered, as a model for NbSe₃. The observed threshold field is associated with depinning of a commensurate part of the charge density, while the excess charge, in form of phase kinks, contributes just to the ohmic conductivity. The characteristic length associated with the frequency generation is one lattice constant.