Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. We show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occurs for frequencies close to the edges of the phonon band. For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinics or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers, or dark breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes an existence result obtained by MacKay and Aubry at small coupling. For an inhomogeneous chain the study of the nonautonomous reduced map is in general far more involved. For the principal part of the reduced recurrence, using the assumption of weak inhomogeneity, we show that homoclinics to 0 exist when the image of the unstable manifold under a linear transformation intersects the stable manifold. This provides a geometrical understanding of tangent bifurcations of discrete breathers. The case of a mass impurity is studied in detail, and our geometrical analysis is successfully compared with direct numerical simulations

A pre-games evaluation of the image impact of the 2012 London Olympics

Along with the World Cup, the Olympics is widely considered to be the most lucrative and sought-after megaevent for governments worldwide, and have thus been described as the ‘the ultimate accolade that a city can earn on the world stage’ (Gold & Gold, 2007: p. 320). For the host, they represent an opportunity to achieve urban and environmental renewal, to boost local and national economies and attract investment, to increase tourism, to present or reinforce local culture and identity, and, to achieve international prominence and/or national prestige through place marketing or even sporting success. A major strategic component in achieving what can be considered a successful Olympics is the image of host-city, in which mega-events provide an ideal opportunity to present the character and culture of the host and work to enhance its domestic and global reputation. There are, however, relatively few studies that deal specifically with the effects of mega-events and the image impact of host countries and cities (Florek et al., 2008)

Progressive Neural Networks

Learning to solve complex sequences of tasks--while both leveraging transfer and avoiding catastrophic forgetting--remains a key obstacle to achieving human-level intelligence. The progressive networks approach represents a step forward in this direction: they are immune to forgetting and can leverage prior knowledge via lateral connections to previously learned features. We evaluate this architecture extensively on a wide variety of reinforcement learning tasks (Atari and 3D maze games), and show that it outperforms common baselines based on pretraining and finetuning. Using a novel sensitivity measure, we demonstrate that transfer occurs at both low-level sensory and high-level control layers of the learned policy

Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic forces. For hard interaction potentials, discrete breathers in this model are known to exist either as ``optic breathers'' with frequencies above the optic band, or as ``acoustic breathers'' with frequencies in the gap between the acoustic and the optic band. In this paper, bifurcations between different types of discrete breathers are found numerically, with the mass ratio m and the breather frequency omega as bifurcation parameters. We identify a period tripling bifurcation around optic breathers, which leads to new breather solutions with frequencies in the gap, and a second local bifurcation around acoustic breathers. These results provide new breather solutions of the FPU system which interpolate between the classical acoustic and optic modes. The two bifurcation lines originate from a particular ``corner'' in parameter space (omega,m). As parameters lie near this corner, we prove by means of a center manifold reduction that small amplitude solutions can be described by a four-dimensional reversible map. This allows us to derive formally a continuum limit differential equation which characterizes at leading order the numerically observed bifurcations.Comment: 30 pages, 10 figure

The fate of the Arctic seaweed Fucus distichus under climate change : an ecological niche modeling approach

Rising temperatures are predicted to melt all perennial ice cover in the Arctic by the end of this century, thus opening up suitable habitat for temperate and subarctic species. Canopy‐forming seaweeds provide an ideal system to predict the potential impact of climate‐change on rocky‐shore ecosystems, given their direct dependence on temperature and their key role in the ecological system. Our primary objective was to predict the climate‐change induced range‐shift of Fucus distichus, the dominant canopy‐forming macroalga in the Arctic and subarctic rocky intertidal. More specifically, we asked: which Arctic/subarctic and cold‐temperate shores of the northern hemisphere will display the greatest distributional change of F. distichus and how will this affect niche overlap with seaweeds from temperate regions? We used the program MAXENT to develop correlative ecological niche models with dominant range‐limiting factors and 169 occurrence records. Using three climate‐change scenarios, we projected habitat suitability of F. distichus – and its niche overlap with three dominant temperate macroalgae – until year 2200. Maximum sea surface temperature was identified as the most important factor in limiting the fundamental niche of F. distichus. Rising temperatures were predicted to have low impact on the species' southern distribution limits, but to shift its northern distribution limits poleward into the high Arctic. In cold‐temperate to subarctic regions, new areas of niche overlap were predicted between F. distichus and intertidal macroalgae immigrating from the south. While climate‐change threatens intertidal seaweeds in warm‐temperate regions, seaweed meadows will likely flourish in the Arctic intertidal. Although this enriches biodiversity and opens up new seaweed‐harvesting grounds, it will also trigger unpredictable changes in the structure and functioning of the Arctic intertidal ecosystem

Effect of Fe intermetallics on microstructure and properties of Al-7Si alloys

The present work deals with the effect of iron intermetallics on the microstructure and mechanical properties of Al-7% Si alloys. Two different iron additions were made, 0.6% Fe and 2% Fe, to study the effect of iron intermetallics on Al-Si alloys. Microstructure property correlations were carried out using SEM-EDS and tensile testing of alloys. Microstructure results show that the rise in iron content significantly increased the average size, thickness and number of intermetallic particles in the alloys. Nano-indentation study shows that the iron intermetallics are too brittle compared with the primary aluminium. Moreover, the hardness and Young’s modulus of iron intermetallics are higher than those of primary aluminium. Tensile test results show that there is no significant difference in strength levels between Al-7%Si and Al-7Si-0.6Fe alloys. However, an increase in iron from 0.6% to 2% resulted in a significant decrease in tensile strength and elongation of the alloys. Two-dimensional SEM studies suggest that the increased number of needle-shaped β-phase intermetallic particles formed because of increased amounts of Fe could be the reason for early failure of the alloy. To further understand the early failure of iron-containing alloys, the fractured tensile specimens were studied using the 3D x-ray tomography technique. XCT results show that the failure in tensile testing of 2% Fe alloy was not mainly due to breaking of brittle β-phase intermetallic particles, but due to the morphology and particle-matrix interface debonding. XCT shows that the needle-shaped particles are long, sharp-edged platelets in 3D, which act as stress raisers for crack initiation and propagation along the interphase

Variation in thermal stress response in two populations of the brown seaweed, Fucus distichus, from the Arctic and subarctic intertidal

It is unclear whether intertidal organisms are ‘preadapted’ to cope with the increase of temperature and temperature variability or if they are currently at their thermal tolerance limits. To address the dichotomy, we focused on an important ecosystem engineer of the Arctic intertidal rocky shores, the seaweed Fucus distichus and investigated thermal stress responses of two populations from different temperature regimes (Svalbard and Kirkenes, Norway). Thermal stress responses at 20°C, 24°C and 28°C were assessed by measuring photosynthetic performance and expression of heat shock protein (HSP) genes (shsp, hsp90 and hsp70). We detected population-specific responses between the two populations of F. distichus, as the Svalbard population revealed a smaller decrease in photosynthesis performance but a greater activation of molecular defence mechanisms (indicated by a wider repertoire of HSP genes and their stronger upregulation) compared with the Kirkenes population. Although the temperatures used in our study exceed temperatures encountered by F. distichus at the study sites, we believe response to these temperatures may serve as a proxy for the species’ potential to respond to climate-related stresses