C. Caroli

A simple model Hamiltonian is proposed for a metal-insulator- metal tunneling junction, which permits the direct calculation of the tunneling current without introducing any effective Hamiltonian. The model rests on the use of localized functions; this procedure avoids the difficult matching problem at the boundary between the barrier and the electrodes. Moreover the use of Kjeldysh's perturbation theory for nonequilibrium system allows an explicit calculation of the current to all orders in the applied bias. It is found that the transfer coefficient appearing in the expression for the current is energy dependent. This model can be systematically extended to include many body effects.

We perform an extensive study of the dry-friction dynamics of a paper-on-paper system. We explore the dynamical phase diagram by systematically varying the relevant control parameters (driving velocity V, slider mass M, and loading machine stiffness k). A set of experimental results gives strong proof that the low-velocity dynamics is controlled by a creep process, in agreement with previous results from rock mechanics and metals [C. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge, 1990), Chap. 2 and references therein; E. Rabinowicz, Proc. Phys. Soc. 71, 668 (1958) and references therein]. At higher velocities, a crossover to inertial dynamics is observed. In each regime, when k is increased, the system bifurcates from periodic stick-slip to steady sliding: in the creep regime, the bifucation is a direct Hopf one; in the inertial regime it becomes subcritical. We identify, from comparison of the time dependence of the static friction coefficient ${\mathrm{\ensuremath{\mu}}}_{\mathit{s}}$(t) and of the velocity dependence of the stationary dynamic one, ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$(V), a memory length of the order of 1 \ensuremath{\mu}m. The V dependence of ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$(V) changes from V weakening to V strengthening at the creep-inertial crossover. We propose a heuristic model of low-velocity friction based on two main ingredients: (i) following and extending the ideas of Ruina [J. Geophys. Res. 88, 10 359 (1983)], we define a phenomenological contact age accounting for the renewal of physical contacts on the scale of the memory length, and (ii) we assume that the dynamics is controlled by the Brownian motion of an effective creeping volume in a pinning potential, the strength of which increases with age.The crossover from creep to inertial motion then naturally appears as the runaway threshold between thermally activated and free motion. The bifurcation analysis in the creep regime is compared in detail with experimental results, yielding a very satisfactory agreement. When confronted with rock mechanics results, this study strongly suggests that low-velocity creep is quite generic; further studies of this process should in particular bear on models of earthquake dynamics.

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between macroscopic hard rough solids, whose main dynamical features are well described by the Rice–Ruina rate and state-dependent constitutive law. We show that it results from two combined effects: (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure and (ii) the geometric aging, i.e. slow growth of the real area of contact via asperity creep interrupted by sliding. Closer analysis leads to identifying a second aging-rejuvenation process, at work within the junctions themselves. We compare the effects of structural aging at such multicontact, very highly confined, interfaces with those met under different confinement levels, namely boundary lubricated contacts and extended adhesive interfaces involving soft materials (hydrogels, elastomers). This leads us to propose a classification of frictional junctions in terms of the relative importance of jamming and adsorption-induced metastability. Solid friction from stick–slip down to pinning and agingAll authorsTristan Baumberger & Christiane Carolihttps://doi.org/10.1080/00018730600732186Published online:28 November 2010Table Download CSVDisplay Table