By Tangora M.C. (ed.)
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Additional info for Algebraic Topology: Oaxtepec 1991
E. α ∼ U/h 1, the necessary length for therefore Pe ∼ αh2 /D. Therefore, if exp(2αtF ) mixing scales as L ∼ log Pe. h Clearly this is much more efficient than the L/h ∼ Pe relationship uncovered earlier. 5 Examples In this section we will describe a collection of examples that come from diverse areas of applications that span a wide range of length and time scales. ’ 14 1 Mixing: physical issues In the next chapter we will see that this paradigm can be realized in a rigorous, mathematical framework as a linked twist map.
Note that in general k and l may be positive or negative integers and so twists may wrap around the torus in either direction. The choice of sign of kl makes a crucial difference to the ensuing results and methods of proof for the mixing properties of the linked twist map. 2 Linked twist maps 34 Having ensured the continuity of F and G we turn to further smoothness properties. Since the identity map is smooth (that is, infinitely times differentiable), the map F will be endowed with the same smoothness properties as the function f only if these smoothness properties also hold on ∂P.
DGSs where all air is replaced by a liquid). 12. After the experiment is done, one remixes the system by shaking (one has to be careful not to unmix) and a new experiment is ready to go. 12 indicate that LGSs and DGSs produce similar segregation patterns. In the DGS case the smaller particles are white and in the LGS the small particles are black. Thus, as opposed to the case of mixing of fluids, the particles tag the location of the largest islands in the flow. This is an area of active investigation at the present time.
Algebraic Topology: Oaxtepec 1991 by Tangora M.C. (ed.)