Gaussian model of explosive percolation in three and higher dimensions

The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple-cubic lattice, in the thermodynamic limit, we report a finite jump of the order parameter, $J=0.415 \pm 0.005$. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension $d_A = 2.5 \pm 0.2$. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with finite number of clusters at the threshold

Percolation with long-range correlated disorder

Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as function of the Hurst exponent $H$ which characterizes the degree of spatial correlation among the occupation of sites. In particular, we study the fractal dimension of the largest cluster and the scaling behavior of the second moment of the cluster size distribution, as well as the complete and accessible perimeters of the largest cluster. Concerning the inner structure and transport properties of the largest cluster, we analyze its shortest path, backbone, red sites, and conductivity. Finally, bridge site growth is also considered. We propose expressions for the functional dependence of the critical exponents on $H$

Watersheds are Schramm-Loewner Evolution curves

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE$_\kappa$, with $\kappa=1.734\pm0.005$, being the only known physical example of an SLE with $\kappa<2$. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT) with central charge $c\approx-7/2$.Comment: 5 pages and 4 figure

Influence of grape rot on the contents of sulfur binding compounds in wine after automated optical grape sorting

In the last years, climate change has played an important role in some wine growing regions because of the increasing hazard of different kinds of bunch rot. Botrytis cinerea is the most important kind of rot on grapes. Beside sensory effects, this rot can influence the content of yeast nutrients, e.g. thiamine, in the must and thus affect the alcoholic fermentation. To get insight into the influence of Botrytis cinerea on the content of sulfur binding compounds formed during the fermentation process in wine, tons of grapes from the Mosel valley were sorted by an automated optical grape sorter, an innovative possibility of grape sorting, in 2011. Wine samples before sulfurisation of the four sorting fractions, namely control (unsorted berries), free-run (juice from opened berries), positive (healthy, intact berries) and negative (rotten berries) were analysed for the sulfur-binding compounds acetaldehyde, pyruvic acid, 2-oxoglutaric acid and for bound sulfur dioxide. The results show that acetaldehyde concentrations were not affected by rot, while pyruvic acid and 2-oxoglutaric acid levels were significantly higher in the negative fractions and lower in the positive fractions. Accordingly, bound sulfur levels were significantly higher in wines from the negative fraction. In conclusion, it could be shown that fractionation of the berries can efficiently help to reduce sulfur binding compounds in wine and thus reduce the addition of sulfur dioxide

Quaternary TDM-PAM as upgrade path of access PON beyond 10Gb/s

A 20 Gb/s quaternary TDM-PAM passive optical network with chirped and non-linear optical transmitters is experimentally demonstrated. The migration from legacy TDM-PONs and the implications of using available 10 Gb/s components are analyzed. We show that a loss budget of 27.3 dB is compatible together with a packet power ratio of 10 dB between loud and soft optical network units. (c) 2012 Optical Society of Americ