Kalikow-type decomposition for multicolor infinite range particle systems

We consider a particle system on $\mathbb{Z}^d$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an algorithm to obtain an explicit construction of a coupling attaining Ornstein's $\bar{d}$-distance for two ordered Ising probability measures.Comment: Published in at http://dx.doi.org/10.1214/12-AAP882 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Microbiology of sediments in lakes of differing degrees of eutrophication

A general survey was carried out on the sediments of seventeen lakes, ranging from oligotrophic to eutrophic, in the English Lake District. Several variables not directly concerned with the population of bacteria were measured to provide background information. Estimates of the total population of bacteria and of the population of filamentous bacteria were made using direct counts with acridine orange and fluorescein di-acetate, and counts by an MPN technique. The counts with acridine orange showed an upward trend with increasing degree of enrichment of the lakes, particularly at the eutrophic end of the spectrum. The distribution pattern obtained with the fluorochrome fluorescein di-acetate was different with an apparent upward trend in the intermediate lakes. The viable counts of the bacterial population in the sediments did not agree with the ranking of the lakes according to published information from the Freshwater Biological Association, although a slight upward trend was observed in the distribution of the viable filamentous bacteria. The preliminary survey led to the selection of three lakes representing the oligrotrophic, mesotrophic and eutrophic states in which a more detailed investigation on the population of filamentous bacteria was made. The profundal and littoral zones of the three lakes were investigated particularly in relation to the different groups of filamentous bacteria and their vertical distribution in the sediments. The groups of filamentous bacteria were described based on morphological and cytochemical tests. A tentative key for identification of filamentous bacteria was devised

A finite-difference scheme for three-dimensional incompressible flows in spherical coordinates

In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P., 1996, A Finite-Difference Scheme for Three-Dimensional Incompressible Flows in Cylindrical Coordinates) for cylindrical coordinates, consists of a change of variables combined with a discretization on a staggered mesh and the special treatment of few discrete terms that remove the singularities of the Navier-Stokes equations at the sphere centre and along the polar axis. This new method alleviates also the time step restrictions introduced by the discretization around the polar axis while the sphere centre still yields strong limitations, although only in very unfavourable flow configurations. The scheme is second-order accurate in space and is verified and validated by computing numerical examples that are compared with similar results produced by other codes or available from the literature. The method can cope with flows evolving in the whole sphere, in a spherical shell and in a sector without any change and, thanks to the flexibility of finite-differences, it can employ generic mesh stretching (in two of the three directions) and complex boundary conditions

Onset of unsteady horizontal convection in rectangle tank at Pr=1Pr=1

The horizontal convection within a rectangle tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of $Ra$ from steady solutions to periodic solutions, and the critical Rayleigh number $Ra_c$ is obtained as $Ra_c=5.5377\times 10^8$ for the middle plume forcing at $Pr=1$, which is much larger than the formerly obtained value. Besides, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's [J. Fluid Mech. 466 (2002) 205] first hypotheses about the destabilization of the flow is numerically proved, i.e. the middle plume forcing can lead to a destabilization of the flow.Comment: 4pages, 6 figures, extension of Chin. Phys. Lett. 2008, 25(6), in pres