How robust is the ring stain for evaporating suspension droplets?

The ring stain is commonly seen when droplets containing particles, such as coffee, are left to dry on a surface: a pinned contact line leads to outward radial flow, which is enhanced by the diverging evaporative flux at the contact line. As shown by Deegan et al. (1997) particles are swept outwards in this flow and create a ring which grows according to a simple power law with time. The final dried width and height of the ring should also be given by power laws of concentration, with both exponent equal to 0.5 provided all particles are in the ring, and the packing factor and ring profile are constant. We use suspensions of polystyrene particles in water with sizes ranging from 200 to 500 nm and initial concentrations c 0 from 0.009% to 1% deposited on glass substrates to investigate these scaling predictions. We vary the drying rate from 0.5 to 5 nl/s using humidity and reduced pressure, use a range of substrates to vary the initial contact angle between 5° and 35°, and invert the droplets to change the direction of gravity. We find that for all but the very lowest pressures, the ring height follows the predicted power law, with exponent equal to 0.50 ± 0.04 and the ring width having an exponent of 0.33 ± 0.05. The discrepancy between the measured and predicted width exponent is accounted for by an observed variation of droplet radius with concentration, and the presence of particles in the center of the droplet. In addition, for low pressures (fast evaporation) the scaling laws no longer hold: the ring is much narrower and there is significant deposition in the center of the droplet, possibly due to reduced particle-enhanced pinning

Root-Weighted Tree Automata and their Applications to Tree Kernels

In this paper, we define a new kind of weighted tree automata where the weights are only supported by final states. We show that these automata are sequentializable and we study their closures under classical regular and algebraic operations. We then use these automata to compute the subtree kernel of two finite tree languages in an efficient way. Finally, we present some perspectives involving the root-weighted tree automata

Bottom Up Quotients and Residuals for Tree Languages

In this paper, we extend the notion of tree language quotients to bottom-up quotients. Instead of computing the residual of a tree language from top to bottom and producing a list of tree languages, we show how to compute a set of k-ary trees, where k is an arbitrary integer. We define the quotient formula for different combinations of tree languages: union, symbol products, compositions, iterated symbol products and iterated composition. These computations lead to the definition of the bottom-up quotient tree automaton, that turns out to be the minimal deterministic tree automaton associated with a regular tree language in the case of the 0-ary trees

Extension, diapirisme et compression en Tunisie centrale : le jebel Es Souda

Le jebel Es Souda est un brachianticlinal, au sein de l'Atlas de Tunisie centrale. Sa structure originale est la résultante d'une tectogenèse compressive polyphasée d'âge mio-plio-quaternaire, superposée à un bombement diapirique, ayant eu lieu au cours du Crétac

The holographic induced gravity model with a Ricci dark energy: smoothing the little rip and big rip through Gauss-Bonnet effects?

We present an holographic brane-world model of the Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet term (GB) in the bulk. We show that an holographic dark energy component with the Ricci scale as the infra-red cutoff can describe the late-time acceleration of the universe. In addition, we show that the dimensionless holographic parameter is very important in characterising the DGP branches, and in determining the behaviour of the Ricci dark energy as well as the asymptotic behaviour of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantom-like behaviour with no big rip if the holographic parameter is strictly larger than 1/2. For smaller values, the brane hits a big rip or a little rip. On the other hand, we have shown that the introduction of the GB term avoids the big rip and little rip singularities on both branches but cannot avoid the appearance of a big freeze singularity for some values of the holographic parameter on the normal branch, however, these values are very unlikely because they lead to a very negative equation of state at the present and therefore we can speak in practice of singularity avoidance. At this regard, the equation of state parameter of the Ricci dark energy plays a crucial role, even more important than the GB parameter, in rejecting the parameter space where future singularities appear.Comment: 11 pages, 8 figures. RevTex4-1. Comments and references added. Version accepted in PR