Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.Comment: 9 page

Rayleigh scattering and atomic dynamics in dissipative optical lattices

We investigate Rayleigh scattering in dissipative optical lattices. In particular, following recent proposals [S. Guibal et al., Phys. Rev. Lett. 78, 4709 (1997); C. Jurczak et al., Phys. Rev. Lett. 77, 1727 (1996)], we study whether the Rayleigh resonance originates from the diffraction on a density grating and is therefore a probe of transport of atoms in optical lattices. It turns out that this is not the case: the Rayleigh line is instead a measure of the cooling rate, while spatial diffusion contributes to the scattering spectrum with a much broader resonance

Shearfree perfect fluids with solenoidal magnetic curvature and a gamma-law equation of state

We show that shearfree perfect fluids obeying an equation of state p=(gamma -1) mu are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.Comment: 11 page

Blind Ghost Imaging

Ghost imaging is an unconventional optical imaging technique that reconstructs the shape of an object combining the measurement of two signals: one that interacted with the object, but without any spatial information, the other containing spatial information, but that never interacted with the object. Ghost imaging is a very flexible technique, that has been generalized to the single-photon regime, to the time domain, to infrared and terahertz frequencies, and many more conditions. Here we demonstrate that ghost imaging can be performed without ever knowing the patterns illuminating the object, but using patterns correlated with them, doesn't matter how weakly. As an experimental proof we exploit the recently discovered correlation between the reflected and transmitted light from a scattering layer, and reconstruct the image of an object hidden behind a scattering layer using only the reflected light, which never interacts with the object. This method opens new perspectives for non-invasive imaging behind or within turbid media.Comment: 5 pages, 4 figure

Correlations between reflected and transmitted intensity patterns emerging from opaque disordered media

The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated. Here we demonstrate experimentally that the reflected and transmitted speckle patterns are correlated, even for opaque media with thickness much larger than the transport mean free path, proving that information survives the multiple scattering process and can be recovered. The existence of mutual information between the two sides of a scattering medium opens up new possibilities for the control of transmitted light without any feedback from the target side, but using only information gathered from the reflected speckle.Comment: 6 pages, 4 figure

Coupled model of root water uptake, mucilage exudation and degradation

Although the prominent role of root mucilage plays a prominent in soil-plant water relations is becoming more and more accepted, many aspects of how mucilage distribution and root water uptake interact with each other remain unexplored. The aims of this study were: i) to measure the effect of soil moisture on mucilage decomposition; ii) to develop a coupled model of root water uptake and mucilage diffusion and degradation during root growth. Mucilage decomposition was measured by adding C4 root mucilage from maize as single pulses to a C3 soil at two different moisture levels. Drought significantly suppressed mucilage mineralization. Opposed to classical solute transport models the water flow in the rhizosphere is affected by the local concentration of mucilage. The model accounts for an increased equilibrium water retention curve, a reduction of hydraulic conductivity at a given water content and a non-equilibrium water retention curve caused by swelling and shrinking dynamics of mucilage. The dispersion coefficient, on the other hand, depends on the water content. The parameters of mucilage diffusion have been fitted to observations on real plants. The model shows that mucilage exuded in wet soils diffuses far from the roots and it is rapidly degraded. On the contrary, mucilage of plants growing in dry soil is not easily degradable and it remains at higher concentrations in a narrow region around the roots, resulting in a marked increase in water content towards the roots as well as to the formation of stable rhizosheath observed in dry soils. This model shows how feedbacks between root water uptake and root exudation could result in adaptation mechanisms of plants to drought

Natural extensions and entropy of α\alpha-continued fractions

We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domain with respect to the density function $(1+xy)^{-2}$. In particular, we show that, for all $0 < \alpha \le 1$, the product of the entropy with the measure of the domain equals $\pi^2/6$. As a key step, we give the explicit relationship between the $\alpha$-expansion of $\alpha-1$ and of $\alpha$

Stochastic resonance in periodic potentials: realization in a dissipative optical lattice

We have observed the phenomenon of stochastic resonance on the Brillouin propagation modes of a dissipative optical lattice. Such a mode has been excited by applying a moving potential modulation with phase velocity equal to the velocity of the mode. Its amplitude has been characterized by the center-of-mass (CM) velocity of the atomic cloud. At Brillouin resonance, we studied the CM-velocity as a function of the optical pumping rate at a given depth of the potential wells. We have observed a resonant dependence of the CM velocity on the optical pumping rate, corresponding to the noise strength. This corresponds to the experimental observation of stochastic resonance in a periodic potential in the low-damping regime