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The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental…

The dynamical behavior caused by dry friction is studied for a spring-block system pulled with constant velocity over a surface. The dynamical consequences of a general type of phenomenological friction law (stick-time dependent static…

A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on horizontal flat surface. We perform…

In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law…

The way granular materials response to an applied shear stress is of the utmost relevance to both human activities and natural environment. One of the their most intriguing and less understood behavior, is the stick-instability, whose most…

The nature of an instability that controls the transition from static to dynamical friction is studied in the the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit…

Friction is central to the motion of active (self-propelled) objects such as bacteria, animals, and robots. While in a viscous fluid friction is described by Stokes's law, objects in contact with other solid bodies are often governed by…

Analytical and numerical modelling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by…

An elastic layer slides on a rigid flat governed by Coulomb's friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick-slip pulses, which transform into opening waves propagating at…

Sliding friction between two dry surfaces is reasonably described by the speed-independent Amonton-Coulomb friction force law. However, there are many situations where the frictional contact points between two surfaces are "active" and may…

We study stochastic motion under a nonlinear frictional force that levels off with increasing velocity. Specifically, our frictional force is of the so-called Coulomb-tanh type. At small speed, it increases approximately linearly with…

Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been…

Amontons' law postulates a monotonic relationship between frictional force and the normal load applied to a sliding contact. This empirical rule, however, fails in systems where internal degrees of freedom - such as structural or electronic…

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…

We consider an active-passive mechanical pair in which the relative motion of the latter is constrained by the mechanical impact. The system dynamics is described by the previously introduced modeling frameworks of force transition and…

We study numerically stick slip motions in a model of blocks and springs being pulled slowly. The sliding friction is assumed to change dynamically with a state variable. The transition from steady sliding to stick-slip is subcritical in a…

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…

Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these…

Recent experiments have revealed a giant "peak effect" in ultrapure high $T_c$ superconductors. Moreover, the new data show that the peak effect coincides exactly with the melting transition of the underlying flux lattice. In this work, we…