On qq- Component Models on Cayley Tree: The General Case

In the paper we generalize results of paper [12] for a $q$- component models on a Cayley tree of order $k\geq 2$. We generalize them in two directions: (1) from $k=2$ to any $k\geq 2;$ (2) from concrete examples (Potts and SOS models) of $q-$ component models to any $q$- component models (with nearest neighbor interactions). We give a set of periodic ground states for the model. Using the contour argument which was developed in [12] we show existence of $q$ different Gibbs measures for $q$-component models on Cayley tree of order $k\geq 2$.Comment: 8 page

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure

The influence of hand positions on biomechanical injury risk factors at the wrist joint during the round-off skills in female gymnastics

The aim of this study was to examine the biomechanical injury risk factors at the wrist, including joint kinetics, kinematics and stiffness in the first and second contact limb for parallel and T-shape round-off (RO) techniques. Seven international-level female gymnasts performed 10 trials of the RO to back handspring with parallel and T-shape hand positions. Synchronised kinematic (3D motion analysis system; 247 Hz) and kinetic (two force plates; 1235 Hz) data were collected for each trial. A two-way repeated measure analysis of variance (ANOVA) assessed differences in the kinematic and kinetic parameters between the techniques for each contact limb. The main findings highlighted that in both the RO techniques, the second contact limb wrist joint is exposed to higher mechanical loads than the first contact limb demonstrated by increased axial compression force and loading rate. In the parallel technique, the second contact limb wrist joint is exposed to higher axial compression load. Differences between wrist joint kinetics highlight that the T-shape technique may potentially lead to reducing these bio-physical loads and consequently protect the second contact limb wrist joint from overload and biological failure. Highlighting the biomechanical risk factors facilitates the process of technique selection making more objective and safe

Seismic slip on an upper-plate normal fault during a large subduction megathrust rupture

Quantification of stress accumulation and release during subduction zone seismic cycles requires an understanding of the distribution of fault slip during earthquakes. Reconstructions of slip are typically constrained to a single, known fault plane. Yet, slip has been shown to occur on multiple faults within the subducting plate1 owing to stress triggering2, resulting in phenomena such as earthquake doublets3. However, rapid stress triggering from the plate interface to faults in the overriding plate has not been documented. Here we analyse seismic data from the magnitude 7.1 Araucania earthquake that occurred in the Chilean subduction zone in 2011. We find that the earthquake, which was reported as a single event in global moment tensor solutions4, 5, was instead composed of two ruptures on two separate faults. Within 12?s a thrust earthquake on the plate interface triggered a second large rupture on a normal fault 30?km away in the overriding plate. This configuration of partitioned rupture is consistent with normal-faulting mechanisms in the ensuing aftershock sequence. We conclude that plate interface rupture can trigger almost instantaneous slip in the overriding plate of a subduction zone. This shallow upper-plate rupture may be masked from teleseismic data, posing a challenge for real-time tsunami warning systems

Free Energy Minimizers for a Two--Species Model with Segregation and Liquid-Vapor Transition

We study the coexistence of phases in a two--species model whose free energy is given by the scaling limit of a system with long range interactions (Kac potentials) which are attractive between particles of the same species and repulsive between different species.Comment: 32 pages, 1 fig, plain tex, typeset twic

Combining stable isotope analysis and conventional techniques to improve knowledge of the diet of the European Roller Coracias garrulus

Diet studies are crucial for understanding the ecology and evolution of species, as well as for establishing appropriate conservation and management strategies. However, they remain methodologically challenging due to variation between seasons, sites, sexes or age groups and even variation between individuals. Due to method-specific characteristics and biases, a combination of existing techniques can overcome the inherent limitations of each technique and provide a more accurate and broad picture of species’ food preferences. Here, we examine diet information obtained using three different assessment methods to better understand the trophic ecology of the European Roller Coracias garrulus, a species targeted by conservation measures in Europe. First, we analysed regurgitated pellets and video recordings to report the diet composition of adult and nestling Rollers, respectively. Secondly, we used stable isotope analysis (SIA) to investigate adult sexual diet segregation as well as to confirm the main findings regarding adult and nestling diets obtained through conventional methods. Based on the analysis of pellets, the diet of adult Rollers was dominated by Coleoptera, while camera images revealed that the diet of nestlings was dominated by Orthoptera, mainly grasshoppers and bush crickets. Blood isotopic signatures of adult and nestling Rollers confirmed the results obtained through pellet and video recording techniques. Of the 45 three methods, pellet analysis contained the most comprehensive trophic information regarding the detectable prey spectrum and prey species contribution, and also provided basic diet information to inform the SIA. Our results also highlight the potential of SIA for assessing intra-specific variation in diet by sampling individuals of known age and sex, which is often unfeasible through conventional approaches. SIA analysis showed no differences in δ13C and δ15N ratios of blood between males and females and a high degree of overlap amongst isotopic niches, suggesting no sex-specific partitioning in resource use. Overall, we showed that the combination of different methods could be used to gain new and clearer insights into avian trophic ecology that are essential for informing habitat management aiming to improve availability of foraging resources