Localized shear generates three-dimensional transport

Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes including mixing, chemical reaction and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID); however, this new mechanism is more rapid and mutually incompatible with RID. We explore its governing impact with both an abstract 2-action flow and a model fluid flow. We show that transitions from one-dimensional (1D) to two-dimensional (2D) and 2D to 3D transport occur based on the relative magnitudes of streamline jumps in two transverse directions.Comment: Copyright 2017 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishin

A Step towards Valuing Utility the Marginal and Cardinal Way

Income has a direct impact on our utility as well as an indirect impact through the goods, services and life events it allows us to purchase. The indirect effect of income is not properly accounted for in existing research that uses measures of cardinal utility for economic analysis. We propose a new approach for appropriately attributing the full effects of income on utility and we show the implications of our approach using a longitudinal dataset that contains reports of subjective wellbeing (SWB). We show that income has a much greater effect on SWB when indirect effects are considered. These results have important implications for how we value the marginal benefits of non-market goods and we explore some of these issues in the papersubjective well-being, utility, happiness, multicollinearity, income, non-market goods

Decay estimates for variable coefficient wave equations in exterior domains

In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.Comment: 15 pages. In the new version, some typos are fixed and a minor correction was made to the proof of Lemma 1

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics, and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points play a more important role than expected. These points represent a bifurcation in local stability and Lagrangian topology. In this study we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of either chaos or confinement depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle-centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.Comment: Accepted version adde

Linking vegetation change, carbon sequestration and biodiversity

1. Despite recent interest in linkages between above- and belowground communities and their consequences for ecosystem processes, much remains unknown about their responses to long-term ecosystem change. We synthesize multiple lines of evidence from a long-term ‘natural experiment’ to illustrate how ecosystem retrogression (the decline in ecosystem processes due to long-term absence of major disturbance) drives vegetation change, and thus aboveground and belowground carbon (C) sequestration, and communities of consumer biota. 2. Our study system involves 30 islands in Swedish boreal forest that form a 5000 year fire-driven retrogressive chronosequence. Here, retrogression leads to lower plant productivity and slower decomposition, and a community shift from plants with traits associated with resource acquisition to those linked with resource conservation. 3. We present consistent evidence that aboveground ecosystem C sequestration declines, while belowground and total C storage increases linearly for at least 5000 years following fire absence. This increase is driven primarily by changes in vegetation characteristics, impairment of decomposer organisms and absence of humus combustion. 4. Data from contrasting trophic groups show that during retrogression, biomass or abundance of plants and decomposer biota decreases, while that of aboveground invertebrates and birds increases, due to different organisms accessing resources via distinct energy channels. Meanwhile, diversity measures of vascular plants and aboveground (but not belowground) consumers respond positively to retrogression. 5. We show that taxonomic richness of plants and aboveground consumers are positively correlated with total ecosystem C storage, suggesting that conserving old growth forests simultaneously maximizes biodiversity and C sequestration. However, we find little observational or experimental evidence that plant diversity is a major driver of ecosystem C storage on the islands relative to other biotic and abiotic factors. 6. Synthesis. Our study reveals that across contrasting islands differing in exposure to a key extrinsic driver (historical disturbance regime and resulting retrogression), there are coordinated responses of soil fertility, vegetation, consumer communities, and ecosystem C sequestration, which all feed back to one another. It also highlights the value of well replicated natural experiments for tackling questions about aboveground-belowground linkages over temporal and spatial scales that are otherwise unachievable