Lyapunov exponents, bifurcation currents and laminations in bifurcation loci

Bifurcation loci in the moduli space of degree $d$ rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier 0 or $e^{i\theta}$. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree $d=2$, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin of fixed period exists

Robust fadeout profile of an evaporation stain

We propose an explanation for the commonly-seen fading in the density of a stain remaining after a droplet has dried on a surface. The density decreases as a power $p$ of the distance from the edge. For thin, dilute drops of general shape this power is determined by a flow stagnation point in the distant interior of the drop. The power $p$ depends on the local evaporation rate J(0) at the stagnation point and the liquid depth $h(0)$ there: $p = 1 - 2 (h(0)/\bar h)(\bar J/J(0))$, where $\bar h$ and $\bar J$ are averages over the drop surface.Comment: 5 pages at journal density 3 figures. v2 has Numerous wording and figure clarifications. Accepted in Europhysics Letters http://www.iop.org/EJ/journal/-page=forthart/0295-5075/

Mechanical tuning of the evaporation rate of liquid on crossed fibers

We investigate experimentally the drying of a small volume of perfectly wetting liquid on two crossed fibers. We characterize the drying dynamics for the three liquid morphologies that are encountered in this geometry: drop, column and a mixed morphology, in which a drop and a column coexist. For each morphology, we rationalize our findings with theoretical models that capture the drying kinetics. We find that the evaporation rate depends significantly on the liquid morphology and that the drying of liquid column is faster than the evaporation of the drop and the mixed morphology for a given liquid volume. Finally, we illustrate that shearing a network of fibers reduces the angle between them, changes the morphology towards the column state, and so enhances the drying rate of a volatile liquid deposited on it