120 research outputs found
Normalization of bundle holomorphic contractions and applications to dynamics
We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic
contractions whose differentials d_0 G_n split regularly. The resonant
relations determining the normal forms hold on the moduli of the exponential
rates of contraction. Our results are actually stated in the framework of
bundle maps.
Such sequences of holomorphic contractions appear naturally as iterated
inverse branches of endomorphisms of CP(k). In this context, our normalization
result allows to precisely estimate the distortions of ellipsoids along typical
orbits. As an application, we show how the Lyapunov exponents of the
equilibrium measure are approximated in terms of the multipliers of the
repulsive cycles.Comment: 29 pages, references added, to appear in Ann. Inst. Fourie
Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of P(k)
We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of P k and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable holomorphic motion of Julia sets which we call equilibrium lamination. We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents or the instability of critical dynamics and analyze how repelling cycles may bifurcate. Our methods deeply exploit the properties of Lyapunov exponents and are based on ergodic and pluripotential theory
Pseudoconvex domains spread over complex homogeneous manifolds
Using the concept of inner integral curves defined by Hirschowitz we
generalize a recent result by Kim, Levenberg and Yamaguchi concerning the
obstruction of a pseudoconvex domain spread over a complex homogeneous manifold
to be Stein. This is then applied to study the holomorphic reduction of
pseudoconvex complex homogeneous manifolds X=G/H. Under the assumption that G
is solvable or reductive we prove that X is the total space of a G-equivariant
holomorphic fiber bundle over a Stein manifold such that all holomorphic
functions on the fiber are constant.Comment: 21 page
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/
Model-based iterative reconstruction in pediatric chest CT: assessment of image quality in a prospective study of children with cystic fibrosis.
BACKGROUND: The potential effects of ionizing radiation are of particular concern in children. The model-based iterative reconstruction VEO(TM) is a technique commercialized to improve image quality and reduce noise compared with the filtered back-projection (FBP) method.
OBJECTIVE: To evaluate the potential of VEO(TM) on diagnostic image quality and dose reduction in pediatric chest CT examinations.
MATERIALS AND METHODS: Twenty children (mean 11.4Â years) with cystic fibrosis underwent either a standard CT or a moderately reduced-dose CT plus a minimum-dose CT performed at 100Â kVp. Reduced-dose CT examinations consisted of two consecutive acquisitions: one moderately reduced-dose CT with increased noise index (NI = 70) and one minimum-dose CT at CTDIvol 0.14Â mGy. Standard CTs were reconstructed using the FBP method while low-dose CTs were reconstructed using FBP and VEO. Two senior radiologists evaluated diagnostic image quality independently by scoring anatomical structures using a four-point scale (1Â =Â excellent, 2Â =Â clear, 3Â =Â diminished, 4Â =Â non-diagnostic). Standard deviation (SD) and signal-to-noise ratio (SNR) were also computed.
RESULTS: At moderately reduced doses, VEO images had significantly lower SD (Pâ<â0.001) and higher SNR (Pâ<â0.05) in comparison to filtered back-projection images. Further improvements were obtained at minimum-dose CT. The best diagnostic image quality was obtained with VEO at minimum-dose CT for the small structures (subpleural vessels and lung fissures) (Pâ<â0.001). The potential for dose reduction was dependent on the diagnostic task because of the modification of the image texture produced by this reconstruction.
CONCLUSIONS: At minimum-dose CT, VEO enables important dose reduction depending on the clinical indication and makes visible certain small structures that were not perceptible with filtered back-projection
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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