双层塑性流动模型中的脱钉
Depinning in a two-layer model of plastic flow
摘要：
我们研究了一个模型的两个层，每个层由一个d维的弹性物体驱动的随机基板，并通过粘性耦合相互作用。对于这个模型，平均场论（即一个完全连接的模型）预测从弹性脱钉到滞后塑性脱钉的无序或粘性耦合增加的过渡。一个功能RG分析表明，任何小的层间粘性耦合不稳定的标准（解耦）弹性脱钉FRG固定点d <= 4，而d > 4的平均场论的大部分方面恢复。在非零速度下的单回路研究表明，对于d<4，在弹性脱钉阈值以下移动状态和钉扎状态共存，对于周期性和非周期性驱动层具有滞后塑性脱钉。准静态的双回路分析揭示了更微妙影响的可能性，包括非周期性物体的新普适性类。我们还研究了d=0，即两个耦合粒子的模型，并表明，滞后并不总是存在的耦合层的周期性稳定状态可以动态不稳定。本文还证明了在任意维d上存在粘性耦合时，稳定的钉扎构型仍然是动力稳定的。此外，层模型的周期性物体是稳定的一个无穷小的相称密度耦合。我们的工作表明，仔细研究相空间中的吸引子及其吸引域对于d= 1，2，3维的情形是必要的。
英文摘要：
We study a model of two layers, each consisting of a d-dimensional elastic object driven over a random substrate, and mutually interacting through a viscous coupling. For this model, the mean-field theory (i.e. a fully connected model) predicts a transition from elastic depinning to hysteretic plastic depinning as disorder or viscous coupling is increased. A functional RG analysis shows that any small inter-layer viscous coupling destablizes the standard (decoupled) elastic depinning FRG fixed point for d <= 4, while for d > 4 most aspects of the mean-field theory are recovered. A one-loop study at non-zero velocity indicates, for d<4, coexistence of a moving state and a pinned state below the elastic depinning threshold, with hysteretic plastic depinning for periodic and non-periodic driven layers. A 2-loop analysis of quasi-statics unveils the possibility of more subtle effects, including a new universality class for non-periodic objects. We also study the model in d=0, i.e. two coupled particles, and show that hysteresis does not always exist as the periodic steady state with coupled layers can be dynamically unstable. It is also proved that stable pinned configurations remain dynamically stable in presence of a viscous coupling in any dimension d. Moreover, the layer model for periodic objects is stable to an infinitesimal commensurate density coupling. Our work shows that a careful study of attractors in phase space and their basin of attraction is necessary to obtain a firm conclusion for dimensions d=1,2,3.
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