Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\mathbb{R}^N\setminus\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is $L$-harmonic, $Lu=0$, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behavior can be presented in a unified way through a suitable global approximation

Boundary fluxes for non-local diffusion

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition

On the best Sobolev trace constant and extremals in domains with holes

We study the dependence on the subset A ⊂ Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p = 2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. © 2005 Elsevier SAS. All rights reserved.Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Deep reefs of the Great Barrier Reef offer limited thermal refuge during mass coral bleaching

Our rapidly warming climate is threatening coral reefs as thermal anomalies trigger mass coral bleaching events. Deep (or "mesophotic") coral reefs are hypothesised to act as major ecological refuges from mass bleaching, but empirical assessments are limited. We evaluated the potential of mesophotic reefs within the Great Barrier Reef (GBR) and adjacent Coral Sea to act as thermal refuges by characterising long-term temperature conditions and assessing impacts during the 2016 mass bleaching event. We found that summer upwelling initially provided thermal relief at upper mesophotic depths (40 m), but then subsided resulting in anomalously warm temperatures even at depth. Bleaching impacts on the deep reefs were severe (40% bleached and 6% dead colonies at 40 m) but significantly lower than at shallower depths (60-69% bleached and 8-12% dead at 5-25 m). While we confirm that deep reefs can offer refuge from thermal stress, we highlight important caveats in terms of the transient nature of the protection and their limited ability to provide broad ecological refuge.XL Catlin Seaview Survey; Waitt Foundation; XL Catlin Group; Underwater Earth; University of Queensland; ARC Discovery Early Career Researcher Award (DECRA) [DE160101433]; Portuguese Science and Technology Foundation (FCT) [SFRH/BPD/110285/2015]; Australian Research Council (ARC

Childhood socioeconomic position and objectively measured physical capability levels in adulthood: a systematic review and meta-analysis

<p><b>Background:</b> Grip strength, walking speed, chair rising and standing balance time are objective measures of physical capability that characterise current health and predict survival in older populations. Socioeconomic position (SEP) in childhood may influence the peak level of physical capability achieved in early adulthood, thereby affecting levels in later adulthood. We have undertaken a systematic review with meta-analyses to test the hypothesis that adverse childhood SEP is associated with lower levels of objectively measured physical capability in adulthood.</p> <p><b>Methods and Findings:</b> Relevant studies published by May 2010 were identified through literature searches using EMBASE and MEDLINE. Unpublished results were obtained from study investigators. Results were provided by all study investigators in a standard format and pooled using random-effects meta-analyses. 19 studies were included in the review. Total sample sizes in meta-analyses ranged from N = 17,215 for chair rise time to N = 1,061,855 for grip strength. Although heterogeneity was detected, there was consistent evidence in age adjusted models that lower childhood SEP was associated with modest reductions in physical capability levels in adulthood: comparing the lowest with the highest childhood SEP there was a reduction in grip strength of 0.13 standard deviations (95% CI: 0.06, 0.21), a reduction in mean walking speed of 0.07 m/s (0.05, 0.10), an increase in mean chair rise time of 6% (4%, 8%) and an odds ratio of an inability to balance for 5s of 1.26 (1.02, 1.55). Adjustment for the potential mediating factors, adult SEP and body size attenuated associations greatly. However, despite this attenuation, for walking speed and chair rise time, there was still evidence of moderate associations.</p> <p><b>Conclusions:</b> Policies targeting socioeconomic inequalities in childhood may have additional benefits in promoting the maintenance of independence in later life.</p&gt

Empirical Models of Transitions between Coral Reef States: Effects of Region, Protection, and Environmental Change

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions

Land-ocean interactions in the coastal zone: Past, present and future

The Land-ocean Interactions in the Coastal Zone (LOICZ) project was established in 1993 as a core project of the International Geosphere-Biosphere Programme (IGBP) to provide the science knowledge to answer "How will changes in land use, sea level and climate alter coastal systems, and what are the wider consequences?" In its first phase of operation (1993-2003) LOICZ began a fundamental investigation focused on biophysical dimensions, including seminal assessments of coastal seas as net sources or sinks of atmospheric CO2, river discharge to the oceans, and biogeochemical modelling. In the second generation of LOICZ (2004-2014), increased attention was paid to the human dimensions of the coast, involving the inclusion of cross-cutting themes such as coastal governance, social-ecological systems, ecological economics and activities around capacity building and the promotion of early career scientists. This paper provides a synthesis of this work and looks forward to the future challenges for the project. With the transition to Future Earth, there is a paradigm shift emerging. The new vision is to support transformation to a sustainable and resilient future for society and nature on the coast, by facilitating innovative, integrated and solutions-oriented science. Realising this vision takes LOICZ into a third generation: to be at the forefront of co-designing, co-producing and co-implementing knowledge for coastal resilience and sustainability. LOICZ as Future Earth Coasts will continue to address 'hotspots' of coastal vulnerability, focusing on themes of dynamic coasts, human development and the coast, and pathways to global coastal sustainability and constraints thereof

27 years of benthic and coral community dynamics on turbid, highly urbanised reefs off Singapore

Coral cover on reefs is declining globally due to coastal development, overfishing and climate change. Reefs isolated from direct human influence can recover from natural acute disturbances, but little is known about long term recovery of reefs experiencing chronic human disturbances. Here we investigate responses to acute bleaching disturbances on turbid reefs off Singapore, at two depths over a period of 27 years. Coral cover declined and there were marked changes in coral and benthic community structure during the first decade of monitoring at both depths. At shallower reef crest sites (3–4 m), benthic community structure recovered towards pre-disturbance states within a decade. In contrast, there was a net decline in coral cover and continuing shifts in community structure at deeper reef slope sites (6–7 m). There was no evidence of phase shifts to macroalgal dominance but coral habitats at deeper sites were replaced by unstable substrata such as fine sediments and rubble. The persistence of coral dominance at chronically disturbed shallow sites is likely due to an abundance of coral taxa which are tolerant to environmental stress. In addition, high turbidity may interact antagonistically with other disturbances to reduce the impact of thermal stress and limit macroalgal growth rates