Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Investigating annual and monthly trends in precipitation structure: an overview across Portugal

This work investigates recent changes in precipitation patterns manifested in long annual and monthly precipitation time series recorded in Portugal. The dataset comprises records from 14 meteorological stations scattered over mainland Portugal and the Portuguese North Atlantic Islands of Madeira and Azores; some of the time series date back to the 19th century. The data were tested for trends using the Mann-Kendall non-parametric test and Sen's non-parametric method, searching both for full monotonic trends over the record period and for partial trends. Results provide no evidence for rejecting the null hypothesis of no trend in annual precipitation, when a monotonic linear model was used. Nevertheless, the analyses of 50 years' moving averages showed an increase over time, in the recent past, for many of the series in mainland Portugal and the Islands. For the longest time series this behaviour was preceded by a decrease over time. The analyses of partial trends in the time series suggested a sequence of alternately decreasing and increasing trends in annual and monthly precipitation, which are sometimes statistically significant. The trend changing points were identified

Numerical modeling of surface runoff and erosion due to moving rainstorms at the drainage basin scale

A physically-based distributed erosion model (MEFIDIS) was applied to evaluate the consequences of storm movement on runoff and erosion from the Alenquer basin in Portugal. Controlled soil flume laboratory experiments were also used to test the model. Nine synthetic circular storms were used, combining three storm diameters (0.5, 1 and 2 times the Alenquer basin's axial length) with three speeds of storm movement (0.5, 1 and 2 m/s); storm intensities were synthesized in order to maintain a constant rainfall depth of 50 mm. The model was applied to storms moving downstream as well as upstream along the basin's axis. In all tests, downstream-moving storms caused significantly higher peak runoff (56.5%) and net erosion (9.1%) than did upstream-moving storms. The consequences for peak runoff were amplified as the storm intensity increased. The hydrograph shapes were also different: for downstream-moving storms, runoff started later and the rising limb was steeper, whereas for upstream moving storms, runoff started early and the rising limb was less steep. Both laboratory and model simulations on the Alenquer basin showed that the direction of storm movement, especially in case of extreme rainfall events, significantly affected runoff and soil loss.http://www.sciencedirect.com/science/article/B6V6C-4K7WTYF-3/1/05f00859098982a6ae43cfee9cc48fe