Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Singular Graphene Metasurfaces

The spatial tunability of the electron density in graphene enables the dynamic engineering of metasurfaces in the form of conductivity gratings, which can bridge the momentum gap between incident radiation and surface plasmons. Here, we discuss singular graphene metasurfaces, whose conductivity is strongly suppressed at the grating valleys. By analytically characterising their plasmonic response via transformation optics, we first review the physical principles underlying these structures, which were recently found to exhibit broadband, tunable THz absorption. We characterise the spectrum with different common substrates and then move to study in further detail how conductivity gratings may be finely tuned by placing an array of charged gold nanowires at sub-micron distance from the graphene

Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.

Avian predators as a biological control system of common vole (Microtus arvalis) populations in NW Spain: experimental set-up and preliminary results

Jareño, D., Paz, A., Arroyo, L., Viñuela, J., Arroyo, B.E., Mougeot, F., Luque-Larena, J.J., Fargallo, J.A

Investigation of Heavy Metals in Zebrafish Tissue by Total Reflection X-ray Fluorescence

Heavy metals are present in the environment, in many consumer products and can be found in food. Some heavy metals like zinc and copper are essential for enzymatic and metabolic function while others like lead and mercury are toxic and interfere with biological pathways. Zebrafish are a very popular model organism for monitoring toxicity of heavy metals and investigating vertebrate development. In this study we explore the possibility of using total reflection X-ray fluorescence spectrometry to analyze histological sections of zebrafish embryos after exposure to nickel and lead. A methacrylate resin embedding protocol and a paraffin embedding protocol were evaluated as possible options for sample preparation for TXRF analysis of zebrafish embryos. It was found that paraffin is the superior material after an alkaline phosphatase stain was introduced. The stain made the normally transparent fish embryo embedded in paraffin clearly visible on the sample reflector material thus allowing for easy positioning and identification of the area of interest

Rotational dynamics induced by low energy binary collisions of quantum droplets

A theoretical analysis of the rotational dynamics induced by off axis binary collisions of quantum droplets constituted by ultracold atoms is reported. We focus on quantum droplets formed by degenerate dilute Bose gases made up from binary mixtures of alkaline atoms under feasible experimental conditions. The stability of the ground state is known to be longer for the chosen heteronuclear gases than for the homonuclear ones. In both cases, we find out that the dynamics seems to privilege a high similarity of the density of each atomic species. However, the evolution of the phase of the corresponding order parameter differs significantly for heteronuclear admixtures. We evaluate the fidelity as a figure of merit for the overlap between the order parameters of each atomic species. Dynamical evidence of the differences between the phase of the order parameters are predicted to manifest in their corresponding linear and angular momenta. We numerically verify that the total angular and linear momenta are conserved both during the collision. Some direct correlations between the Weber number and the impact parameter with the distribution of the dynamical variables are established.Comment: 12 pages, 6 figure

New directions in management strategy evaluation through cross-fertilisation between fisheries science and terrestrial conservation

et al.On 1 and 2 June 2010, an international meeting was held at the University of Paris Sud XI, France, organized within the framework of the EU FP7 consortium project HUNT, to bring together fisheries and conservation scientists to discuss a unified framework for the future of management strategies for harvested species.E.J.M.G. acknowledges the support of a Royal Society Wolfson Research Merit award. This workshop was supported by the European Commission under the HUNT project of the 7th Framework Programme for Research and Technological Development.Peer Reviewe