The Mayer series of the Lennard-Jones gas: improved bounds for the convergence radius

We provide a lower bound for the convergence radius of the Mayer series of the Lennard-Jones gas which strongly improves on the classical bound obtained by Penrose and Ruelle 1963. To obtain this result we use an alternative estimate recently proposed by Morais et al. (J. Stat. Phys. 2014) for a restricted class of stable and tempered pair potentials (namely those which can be written as the sum of a non-negative potential plus an absolutely integrable and stable potential) combined with a method developed by Locatelli and Schoen (J. Glob. Optim. 2002) for establishing a lower bound for the minimal interatomic distance between particles interacting via a Morse potential in a cluster of minimum-energy configurations

Non-Euclidean ideal spectrometer

We describe the mathematical scheme for an anomaly-free ideal spectrometer, based on a 2-dimensional plane medium with conical regions of bounded slope. Moreover, the construction may be realised in many different configurations.Comment: 9 pages, 5 figure

Fish-based groups for ecological assessment in rivers: the importance of environmental drivers on taxonomic and functional traits of fish Assemblages

The use of river-types is of practical value, serving as groups for which assessment procedures can be developed and applied. An abiotic typology was set by the Portuguese Water Agency, mainly based on 6 major morphoclimatic regions. However, to be biologically meaningful, this typology should fit the distribution patterns of the biological quality elements communities proposed in Water Framework Directive under the lowest possible human pressure. This study aimed to identify and characterize fish-based geographical groups for continental Portugal and their environmental and geographical discriptors, using taxonomic and functional traits. Sampling took place between 2004 and 2006 during Spring. Fish fauna from 155 reference sites was analysed using a multivariate approach. Cluster Analysis on fish composition identified 10 fish-groups, expressing a clear correspondence to the river basin level, due to the restrict basin distribution of many species. Groups showed a wider aggregation in 4 regions with a larger geographical correspondence, statistically supported by Similarity Analysis, both on fish composition and mostly on fish metrics/guilds. Principal Components Analysis revealed major environmental drivers associated to fish-groups and fish-regions. Fish-groups were hierarchically grouped over major and local regions, expressing a large-scale response to a North-South environmental gradient defined by temperature, precipitation, mineralization and altitude, and a regional scale response mainly to drainage area and flow discharge. From North to South, fish-regions were related to the morphoclimatic regions. Results contributed to reduce redundance in abiotic river-types and set the final typology for Portuguese rivers, constituting a fundamental tool for planning and managing water resources

Truncation of long-range percolation model with square non-summable interactions

We consider some problems related to the truncation question in long-range percolation. It is given probabilities that certain long-range oriented bonds are open; assuming that this probabilities are not summable, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. This question is still open if the set of vertices is $\Z^2$. We give some conditions in which the answer is affirmative. One of these results generalize the previous result in [Alves, Hil\'ario, de Lima, Valesin, Journ. Stat. Phys. {\bf 122}, 972 (2017)]

Long-range contact process and percolation on a random lattice

We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also study an analogous oriented percolation model on the hyper-cubic lattice, here there is a special direction where long-range oriented bonds are allowed; the range of all vertices are given by an i.i.d. sequence of random variables with common distribution $N$. For both models, we prove some results about the existence of a phase transition in terms of the distribution $N$