Dynamics of a 1-D model for the emergence of the plasma edge shear flow layer with momentum conserving Reynolds stress

A one-dimensional version of the second-order transition model based on the sheared flow amplification by Reynolds stress and turbulence supression by shearing is presented. The model discussed in this paper includes a form of the Reynolds stress which explicitly conserves momentum. A linear stability analysis of the critical point is performed. Then, it is shown that the dynamics of weakly unstable states is determined by a reduced equation for the shear flow. In the case in which the flow damping term is diffusive, the stationary solutions are those of the real Ginzburg-Landau equation.Comment: 21 pages, 8 figure

Distribution of skates and sharks in the North Sea: 112 years of change

How have North Sea skate and shark assemblages changed since the early 20th century when bottom trawling became widespread, whilst their environment became increasingly impacted by fishing, climate change, habitat degradation and other anthropogenic pressures? This article examines long-term changes in the distribution and occurrence of the elasmobranch assemblage of the southern North Sea, based on extensive historical time series (1902–2013) of fishery-independent survey data. In general, larger species (thornback ray, tope, spurdog) exhibited long-term declines, and the largest (common skate complex) became locally extirpated (as did angelshark). Smaller species increased (spotted and starry ray, lesser-spotted dogfish) as did smooth-hound, likely benefiting from greater resilience to fishing and/or climate change. This indicates a fundamental shift from historical dominance of larger, commercially valuable species to current prevalence of smaller, more productive species often of low commercial value. In recent years, however, some trends have reversed, with the (cold-water associated) starry ray now declining and thornback ray increasing. This shift may be attributed to (i) fishing, including mechanised beam trawling introduced in the 1960s–1970s, and historical target fisheries for elasmobranchs; (ii) climate change, currently favouring warm-water above cold-water species; and (iii) habitat loss, including potential degradation of coastal and outer estuarine nursery habitats. The same anthropogenic pressures, here documented to have impacted North Sea elasmobranchs over the past century, are likewise impacting shelf seas worldwide and may increase in the future; therefore, parallel changes in elasmobranch communities in other regions are to be expected

Distributed Generation and Resilience in Power Grids

We study the effects of the allocation of distributed generation on the resilience of power grids. We find that an unconstrained allocation and growth of the distributed generation can drive a power grid beyond its design parameters. In order to overcome such a problem, we propose a topological algorithm derived from the field of Complex Networks to allocate distributed generation sources in an existing power grid.Comment: proceedings of Critis 2012 http://critis12.hig.no

Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.Comment: 14 pages, 1 figure. References added. Published versio

Fractional generalization of Fick's law: a microscopic approach

In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First, finite characteristic length and time scales associated to the dominant transport process must exist. Secondly, the transport mechanism must satisfy a microscopic symmetry: global reversibility. Global reversibility is often satisfied in nature. However, many complex systems exhibit a lack of finite characteristic scales. In this Letter we show how to construct a generalization of the inhomogeneous Fick law that does not require the existence of characteristic scales while still satisfying global reversibility.Comment: 4 pages. Published versio

Does size matter?

Failures of the complex infrastructures society depends on having enormous human and economic cost that poses the question: Are there ways to optimize these systems to reduce the risks of failure? A dynamic model of one such system, the power transmission grid, is used to investigate the risk from failure as a function of the system size. It is found that there appears to be optimal sizes for such networks where the risk of failure is balanced by the benefit given by the size

Kinetic description of avalanching systems

Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth magnetosphere.Comment: 9 page