Mathematics

New Physics Research Research from University of Wisconsin Outlined

  2012 APR 17 - (VerticalNews.com) -- A report, "Moving walls accelerate mixing," is newly published data in Physical Review E, Statistical, Nonlinear, and Soft Matter Physics. "Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario, the decay rate of the concentration profile of a passive scalar should be exponential in time," scientists in Madison, Wisconsin report.

  "In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit," wrote J.L. Thiffeault and colleagues, University of Wisconsin.

  The researchers concluded: "The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall."

  Thiffeault and colleagues published their study in Physical Review E, Statistical, Nonlinear, and Soft Matter Physics (Moving walls accelerate mixing. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2011;84(3 Pt 2):036313).

  For additional information, contact J.L. Thiffeault, Dept. of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States.

  Keywords: City:Madison, State:Wisconsin, Country:United States, Region:North and Central America, Physics Research.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2012, VerticalNews Mathematics via VerticalNews.com.