We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity.

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In this article we show that models of flows in DNA microarrays generated by pulsed source-sink pairs can be studied as linked twist maps. The significance of this is that it enables us to relate the flow to mathematically precise notions of chaotic mixing that can be realized through specific design criteria. We apply these techniques to three different mixing protocols, two of which have been previously described in the literature, and we are able to isolate the features of each mixer that lead to "good" or "bad" mixing. Based on this, we propose a new design to generate a "well-mixed" flow in a DNA microarray.

The theory of the elastic contact of two bodies developed by Hertz [1] is generalized including the contribution of viscous effects to the total stress. A nonlinear differential equation for the compression is derived for particles with arbitrary curvature of their surfaces and is solved numerically for spherical particles. The resulting dependence of the normal restitution coefficient on the impact velocity is calculated and compared with experimental data for ice at low temperatures [2, 3]. A good agreement is found which allows to estimate unknown material constants in certain cases. An astrophysical application of the results is briefly discussed for the especially interesting case of icy particles in planetary rings

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