Pinning-depinning Transition Research Articles

AC susceptibility study of the intergranular irreversibility line in BSCCO ceramic superconductors

The intergranular irreversibility line of granular BSCCO-2223 sample was found by measuring the AC susceptibility. The data are compared with the analogous ones for a YBCO ceramic. The measured values agree with the ones determined through the giant flux-creep theory adapted to the intergranular case, choosing appropriate parameters. This result suggests that the change from non-dissipative to dissipative states can be regarded as an intergranular pinning-depinning transition.

Theory of transient creep in the L1 2 intermetallic compounds displaying the yield strength anomaly

A theory of transient creep in the L1 2 intermetallic alloys displaying the yield strength anomaly is presented. The theory is based on the hypothesis that the mobile a〈101〉 superdislocations undergo a pinning-depinning transition, displaying critical behavior at a critical stress. The areal-velocity scaling function, which describes the average, time-dependent velocity profile of a dislocation as it propagates through the crystal, is introduced. The theory is compared with preliminary experiments. It is argued that the measurement of transient creep allows one to determine information concerning the deformation history of the sample.

Criticality in the plastic deformation of L12 intermetallic compounds.

It is argued that dislocations in the [ital L]1[sub 2] intermetallic compounds displaying the yield strength anomaly undergo a stress-driven pinning-depinning transition. The transition is from a dynamic phase in which a moving dislocation becomes immobile to a dynamic phase in which a moving dislocation, in an infinite medium, remains mobile for all time. The distribution of event times and areas, where an event'' is the mobilization and subsequent immobilization of a dislocation, is related to measurements of the primary creep transient. At the critical point of the proposed transition, the distribution of events becomes scale invariant. A simple scaling hypothesis connects the scaling behavior of the transition to the time dependence of the creep tests. A simplified model of dislocation motion is presented and used to study the properties of the transition. The properties so calculated are not obviously consistent with the published [ital interpretations] of experiments, but are consistent with the published [ital data]. A reinterpretation of those experiments is proposed.

Nonanalytic twist maps and Frenkel-Kontorova models

We give a review of our recent works on a class of twist maps and Frenkel-Kontorova (FK) models in which the external potential function is nonanalytic (C 1) and endowed with a variable degree of inflection z. When z > 3, recurrence of invariant curves has been observed. An “inverse residue criterion” for the reappearance of an invariant curve — complementary to the “residue criterion” for the disappearance of an invariant curve — is introduced to make a precise determination of the reappearance point. We have also studied the local and global scaling behaviors of these curves. The critical exponents, the singularity spectrum, and the generalized dimensions are found to vary with z when 2 ⩽ z < 3, but remain the same for z ⩾ 3. The degree of inflection thus plays a role reminiscent of that of dimensionality in phase transitions with z = 2 and 3 corresponding respectively to the lower and upper critical dimensions. When the same nonanalytic function is substituted for the sinusoidal external potential in the standard FK model, the same conclusions are reached: there exists a sequence of pinning-depinning transitions, and the critical exponents of the phonon gap, the coherence length, and the Peierls-Nabarro barrier all show the same dependence on z.

Renormalization-group treatment of a pinning-depinning transition in an incommensurate structure

A new type of renormalization-group approach is suggested to treat the structure and properties of the Frenkel-Kontorova (discrete sine-Gordon) model ground states. Special attention is devoted to the incommensurate structures where the transition by breaking of analyticity of the hull function (pinning-depinning transition) occurs when the strength of the periodic potential is varied. The method gives for a particular incommensurability-the 'golden mean' one-a critical value of the potential strength one-and-a-half times larger than the exact value obtained by Aubry et al. (1982, 1983) by numerical methods. The critical index of correlation length coincides within a few per cent accuracy with its exact value.

Computer simulations of a vortex line motion in type-II superconductors

We study a vortex line motion in type-II superconductors which is driven by vortex line tension, Lorentz force, pinning force and thermal fluctuations. On the basis of the local stochastic differential equation for the vortex motion with no torsion approximation, several computer simulations are performed to investigate the pinning behavior of the vortex line. It is shown that at zero temperature for sufficiently high impurity concentration the vortex line is trapped by random impurities, that is, the collective pinning occurs, and the temperature effect leads to the pinning-depinning transition at a certain temperature.

Self-organized critical behavior in pinned flux lattices.

We study the response of pinned flux lattices, under small perturbations in the driving force, below and close to the pinning-depinning transition. For driving Lorentz forces below ${F}_{c}$ (the depinning force at which the whole flux lattice slides), the system has instabilities against small force increases, with a power-law distribution characteristic of self-organized criticality. Specifically, $D(d)\ensuremath{\sim}{d}^{\ensuremath{-}1.3}$, where $d$ is the displacement of a flux line after a very small force increase. We also study the initial stages of the motion of the lattice once the driving force overcomes the pinning forces.

Scaling in cascades of transitions.

We study the new scaling exponents associated with the series of transitions corresponding to breakup of a Kol'ogorov-Arnol'd-Moser torus in a standard-type map. This map models a variety of transitions in incommensurate systems such as metal-insulator or pinning-depinning transitions. Our study provides evidences for the global scaling in addition to the local scaling properties of the fractal phase diagram.

Generalised depinning transition in a solid-on-solid model

The pinning of a domain wall by a row of weakened bonds in the interior of a planar Ising ferromagnet is studied in the solid-on-solid limit. Analysing a continuum version of the model the authors show that a pinning-depinning transition occurs whenever the couplings on the two sides of the defect are different. The roughening transition found by Abraham is contained as a special case.