Fermionic Corrections to Fluid Dynamics from BTZ Black Hole

We reconstruct the complete fermionic orbit of the non-extremal BTZ black hole by acting with finite supersymmetry transformations. The solution satisfies the exact supergravity equations of motion to all orders in the fermonic expansion and the final result is given in terms of fermionic bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes equations and a set of new differential equations from Rarita-Schwinger equation. We compute the boundary energy-momentum tensor and we interpret the result as a perfect fluid with a modified definition of fluid velocity. Finally, we derive the modified expression for the entropy of the black hole in terms of the fermionic bilinears.Comment: 21 pages, Latex2e, no figure

On the adhesion of particles to a cell layer under flow

The non-specific adhesion of spherical particles to a cell substrate is analyzed in a parallel plate flow chamber, addressing the effect of the particle size. Differently from other experiments, the total volume of the injected particles has been fixed, rather than the total number of particles, as the diameter d of the particles is changed from 500 nm up to 10 $\mu$m. From the analysis of the experimental data, simple and instructive scaling adhesion laws have been derived showing that (i) the number of particles adherent to the cell layer per unit surface decreases with the size of the particle as d^(-1.7) ; and consequently (ii) the volume of the particles adherent per unit surface increases with the size of the particles as d^(+1.3). These results are of importance in the "rational design" of nanoparticles for drug delivery and biomedical imaging.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Fermionic Wigs for BTZ Black Holes

We compute the wig for the BTZ black hole, namely the complete non-linear solution of supergravity equations with all fermionic zero modes. We use a "gauge completion" method starting from AdS_3 Killing spinors to generate the gravitinos fields associated to the BH and we compute the back-reaction on the metric. Due to the anticommutative properties of the fermionic hairs the resummation of these effects truncates at some order. We illustrate the technique proposed in a precedent paper in a very explicit and analytical form. We also compute the mass, the angular momentum and other charges with their corrections.Comment: 11 pages, no figure

Fermions, Wigs, and Attractors

We compute the modifications to the attractor mechanism due to fermionic corrections. In N=2, D=4 supergravity, at the fourth order, we find a new contribution to the horizon values of the scalar fields of the vector multiplets.Comment: v2 : 1+11 pages; paper reorganized in Sections; Sec. 5 added, with detailed treatment of the axion-dilaton model; some typos fixed and references adde

Resummation of perturbation series and reducibility for Bryuno skew-product flows

We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.Comment: 30 pages, 12 figure

Fractional Lindstedt series

The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter, i.e. they are not analytic functions of the perturbation parameter. However rather generally quasi-periodic motions whose frequencies satisfy only one rational relation ("resonances of order 1") admit formal perturbation expansions in terms of a fractional power of the perturbation parameter, depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation.Comment: 40 pages, 6 figure