87 research outputs found
Lyapunov exponents, bifurcation currents and laminations in bifurcation loci
Bifurcation loci in the moduli space of degree rational maps are shaped
by the hypersurfaces defined by the existence of a cycle of period and
multiplier 0 or . 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 , 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 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 depends on the local evaporation rate J(0)
at the stagnation point and the liquid depth there: , where and 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
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