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3D view of the trajectory (solid red curve) leaving and landing out and in the SM (yellow-green surface), the black part diverging on S displays the 2D flow in its "non slow" regime.

3D view of the trajectory (solid red curve) leaving and landing out and in the SM (yellow-green surface), the black part diverging on S displays the 2D flow in its "non slow" regime.

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Catastrophes of all kinds happen all the time in the real world. They can be roughly defined as short duration-large amplitude events, following and followed by long periods of “ripening” of the system under consideration. They are obviously related to a class of phenomena called sometime “relaxation” oscillations. This makes them a priori a good s...

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... Generation of motion of liquid droplets in contact with a surface is not only important in various technological settings, it also has a significant philosophical underpinning in that it forms an interesting paradigm for non-equilibrium thermodynamics. For example, the evolution of noise resulting from pinning depinning transitions could be used to understand the physics of critical dynamics 43 , in which the development of fluctuation announces whether a system would speed up or slow down critically, long before such a catastrophe actually happens. Barrier crossing experiments with a drop could also serve as a model system with which to study the physics of Kramers' transition involving soft deformable particles. ...
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A liquid drop moves on a solid surface if it is subjected to a gradient of wettability or temperature. However the pinning defects on the surface manifesting in terms of a wetting hysteresis, or a first order non-linear friction, limits the motion in the sense that a critical size has to be exceeded for a drop to move. The effect of hysteresis can, however, be mitigated by an external vibration that can be either structured or stochastic, thereby creating a directed motion of the drop. Many of the well-known features of rectification, amplification and switching that are generic to electronics can be engineered with such types of movements. A specific case of interest is the random coalescence of drops on a surface that gives rise to a self-generated noise. This noise overcomes the pinning potential diffusively, thereby generating a random motion of the coalesced drops. Randomly-moving coalesced drops themselves exhibit a purely diffusive flux when a boundary is present to eliminate them by absorption. With the presence of a bias, the coalesced drops execute a diffusive drift motion that can have useful application in various water and thermal management technologies.