Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems

For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker. We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents.Comment: 6 pages, 5 figures, 1 tabl

Noro-Frenkel scaling in short-range square well: A Potential Energy Landscape study

We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth $-u_0$), as a function of the range of attraction $\Delta$ to provide thermodynamic insights of the Noro and Frenkel [ M.G. Noro and D. Frenkel, J.Chem.Phys. {\bf 113}, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a {\it vibrational} ($\Delta$-dependent) and a {\it floppy} ($\Delta$-independent) component. We also show that the partition function is a function of $\Delta e^{\beta u_o}$, explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).Comment: 4 pages, 4 figures accepted for publication on PR

Improvement of performances of continuous biological water treatment with periodic solutions

We study periodic solutions of the chemostat model under an integral constraint, either on the flow rate (Pb. 1) or on the substrate concentration (Pb. 2). We give conditions on the growth kinetics for which it is possible to improve the averaged water quality (Pb. 1) or the total quantity of treated water (Pb. 2) over a given time period, compared to steady-state. When this is possible, we characterize optimal periodic solutions and show a duality between the two optimization problems. The results are illustrated on four types of growth kinetics, given by Monod, Haldane, Hill and Contois functions

Non-equilibrium two-phase coexistence in a confined granular layer

We report the observation of the homogenous nucleation of crystals in a dense layer of steel spheres confined between two horizontal plates vibrated vertically. Above a critical vibration amplitude, two-layer crystals with square symmetry were found to coexist in steady state with a surrounding granular liquid. By analogy to equilibrium hard sphere systems, the phase behavior can be explained through entropy maximization. However, dramatic non-equilibrium effects are present, including a significant difference in the granular temperatures of the two phases.Comment: 4 pages, 3 figures, RevTex4 forma

Scaling of dynamics with the range of interaction in short-range attractive colloids

We numerically study the dependence of the dynamics on the range of interaction $\Delta$ for the short-range square well potential. We find that, for small $\Delta$, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive glass line and the liquid-gas line does not depend on $\Delta$. This proves that in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.Comment: 4 pages, 4 figure

Crystallization Mechanism of Hard Sphere Glasses

In supercooled liquids, vitrification generally suppresses crystallization. Yet some glasses can still crystallize despite the arrest of diffusive motion. This ill-understood process may limit the stability of glasses, but its microscopic mechanism is not yet known. Here we present extensive computer simulations addressing the crystallization of monodisperse hard-sphere glasses at constant volume (as in a colloid experiment). Multiple crystalline patches appear without particles having to diffuse more than one diameter. As these patches grow, the mobility in neighbouring areas is enhanced, creating dynamic heterogeneity with positive feedback. The future crystallization pattern cannot be predicted from the coordinates alone: crystallization proceeds by a sequence of stochastic micro-nucleation events, correlated in space by emergent dynamic heterogeneity.Comment: 4 pages 4 figures Accepted for publication in Phys. Rev. Lett., April 201

Astrometry with "Carte du Ciel" plates, San Fernando zone. I. Digitization and measurement using a flatbed scanner

We present an original method of digitizing and astrometrically reducing "Carte du Ciel" plate material using an inexpensive flatbed scanner, to demonstrate that for this material there is an alternative to more specialized measuring machines that are very few in number and thus not readily available. The sample of plates chosen to develop this method are original "Carte du Ciel" plates of the San Fernando zone, photographic material with a mean epoch 1903.6, and a limiting photographic magnitude ~14.5, covering the declination range of -10 < dec < -2. Digitization has been made using a commercial flatbed scanner, demonstrating the internal precision that can be attained with such a device. A variety of post-scan corrections are shown to be necessary. In particular, the large distortion introduced by the non-uniform action of the scanner is modelled using multiple scans of each plate. We also tackle the specific problems associated with the triple-exposure images on some plates and the grid lines present on all. The final measures are reduced to celestial coordinates using the Tycho-2 Catalogue. The internal precision obtained over a single plate, 3microns ~ 0.18" in each axis, is comparable to what is realized with similar plate material using slower, less affordable, and less widely available conventional measuring machines, such as a PDS microdensitometer. The accuracy attained over large multi-plate areas, employing an overlapping plate technique, is estimated at 0.2".Comment: 16 pages, 19 figures and 3 tables. Accepted for publication in A&

Is there a reentrant glass in binary mixtures?

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component only occurs if the ratio $\alpha$ of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For $\alpha \approx 1$, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with two-component mode coupling theory. For $\alpha \ll 1$, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode coupling theory.Comment: 4 pages, 3 figure

Configurational entropy of hard spheres

We numerically calculate the configurational entropy S_conf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires less assumptions than the previous methods [R.J. Speedy, Mol. Phys. 95, 169 (1998)]. We find that S_conf is a decreasing function of packing fraction f and extrapolates to zero at the Kauzmann packing fraction f_K = 0.62, suggesting the possibility of an ideal glass-transition for hard spheres system. Finally, the Adam-Gibbs relation is found to hold.Comment: 10 pages, 6 figure