Depinning force

Studies based on the Frenkel-Kontorova model reveal that static friction depends on the strength of interactions and structural commensurability between the surfaces in contact. For surfaces in incommensurate contact, there is a critical strength, b, below which the depinning force becomes zero and static friction disappears, i.e., the chain starts to slide if an infinitely small force F is applied (cf. Section 3). This is understandable from the energetic point of view that the interfacial atoms in an incommensurate system can hardly settle in any potential minimum, or the energy barrier, which prevents the object from moving, can be almost zero. 

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

Due to the continuous evaporation of the droplet, the force induced by surface tension of the extracted liquid surface overcomes the pinning force. As a result, the contact line depins from the ring of deposited solute and jumps... 

The weak interchain coupling orders the modulated structure three-dimen-sionally at the Peierls transition temperature, Tp. The force due to an applied electric field, within regions where the CDW is coherent, is counterbalanced by the pinning force of impurities or other defects. For high-purity crystals the application of small electric fields may depin the CDW from the lattice, and the modulated structure slides as a whole. 

Recently, the breakup of free spiral waves has been observed in the numerical simulations of reaction-diffusion models [42-46]. This effect is principally of the same nature as breaking (or spontaneous depinning) of a pinned spiral wave. The main question is here what induces breaking of the wave front at a certain distance from the free tip. In some of the stimulations (e.g. [42-45]), the breakup is preceded by the onset of meandering which might actually produce the inhomogeneities of the residual inhibitor concentration that force the wave to break. 

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