Array-enhanced friction in the periodic stick-slip motion of nonlinear oscillators

Transition from Static to Dynamic Friction in an Array of Frictional Disks

The nature of an instability that controls the transition from static to dynamical friction is studied in the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit and Newtonian dynamics can be employed without any phenomenological assumptions. We show that an oscillatory instability that had been discovered recently is responsible for the transition, allowing individual disks to spontaneously reach the Coulomb limit and slide with dynamic friction. The transparency of the model allows a full understanding of the phenomenon, including the speeds of the waves that travel from the trailing to the leading edge and vice versa.

Non-Lipschitzian control algorithms for extended mechanical systems

We derive the properties of a general control algorithm [Braiman et al., Phys. Rev. Lett. 90, 094301 (2003)] for quantities describing global features of nonlinear extended mechanical systems. The control algorithm is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that (i) certain average quantities of the controlled system can be driven-exactly or approximately-towards desired targets which become linearly stable attractors for the system's dynamics; (ii) the basins of attraction of these targets are reached in very short times; and (iii) while within reasonably broad ranges the time-scales of the control and of the intrinsic dynamics may be quite different, this disparity does not affect significantly the overall efficiency of the proposed scheme, up to natural fluctuations.

Optimal control of the transient behavior of coupled solid-state lasers

We apply optimal control theory to substantially reduce transient times for transitions between in-phase and out-of-phase states in coupled solid-state lasers. The control is a time-varying optical field that is injected into the cavities of each laser. We have analytically derived the optimal control and numerically solved the optimality system. Numerical simulations indicate that transient times can be significantly reduced upon increasing the injection strength very briefly.

Control of friction at the nanoscale

We propose a new algorithm to control frictional dynamics of a small array of particles towards preassigned values of the average sliding velocity. The control is based on the concepts of non-Lipschitzian dynamics and terminal attractor. Extensive numerical simulations illustrate the robustness, efficiency, and convenience of the algorithm.

Collective topological dynamics in the frenkel-kontorova chains

Topological dynamics of an array of harmonically coupled damped dc-driven nonlinear oscillators are studied by introducing a dynamical contraction factor and a deviation factor. Different dynamical transitions are identified, and topological changes for these transitions are studied. A bifurcation from the kink state to the kink-antikink-pair state is found, which relates the topological change to the spatiotemporal dynamics of the system. The presence of antikinks leads to the extension of the localized kink, and collisions of kinks and antikinks induce strong oscillations of the topology of the array.

Friction and noise-induced coherent structures in boundary lubrication

We examine the effect of stick-slip boundary conditions on the friction generated by a molecularly thin layer of a liquid lubricant separating two plates. For one-dimensional compressible flows, noise-induced coherent dissipative structures on a micron scale are generated due to cooperation between the external drive and the thermal noise. As a function of the thermal noise these structures show a peak in their amplitudes similar to stochastic resonance. At low velocities a reduction in friction with increasing thermal noise is observed.

Tuning friction with noise and disorder

We present numerical and experimental evidence which demonstrates that under certain conditions friction can be reduced by spatial disorder and/or thermal noise. We discuss possible mechanisms for this behavior.