Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Contrasting arbuscular mycorrhizal communities colonizing different host plants show a similar response to a soil phosphorus concentration gradient

High soil phosphorus (P) concentration is frequently shown to reduce root colonization by arbuscular mycorrhizal (AM) fungi, but the influence of P on the diversity of colonizing AM fungi is uncertain. We used terminal restriction fragment length polymorphism (T-RFLP) of 18S rDNA and cloning to assess diversity of AM fungi colonizing maize (Zea mays), soybean (Glycene max) and field violet (Viola arvensis) at three time points in one season along a P gradient of 10280mgl1 in the field. Percentage AM colonization changed between sampling time points but was not reduced by high soil P except in maize. There was no significant difference in AM diversity between sampling time points. Diversity was reduced at concentrations of P > 25mgl1, particularly in maize and soybean. Both cloning and T-RFLP indicated differences between AM communities in the different host species. Host species was more important than soil P in determining the AM community, except at the highest P concentration. Our results show that the impact of soil P on the diversity of AM fungi colonizing plants was broadly similar, despite the fact that different plants contained different communities. However, subtle differences in the response of the AM community in each host were evident.

Up-gradient eddy fluxes of potential vorticity near the subtropical jet

The role of eddy fluxes in the general circulation is often approached by treating eddies as (macro)turbulence. In this approach, the eddies act to diffuse certain quasiconservative quantities, such as potential vorticity (PV), along isentropic surfaces in the free atmosphere. The eddy fluxes are determined primarily by the eddy diffusivities and are necessarily down-gradient of the basic state PV field. Support for the (macro)turbulence approach stems from the fact that the eddy fluxes of PV in the free atmosphere are generally down-gradient in the long-term mean. Here we call attention to a pronounced and significant region of upgradient eddy PV fluxes on the poleward flank of the jet core in both hemispheres. The region of up-gradient (i.e., notionally “antidiffusive”) eddy PV fluxes is most pronounced during the winter and spring seasons and partially contradicts the turbulence approach described above. Analyses of the PV variance (potential enstrophy) budget suggest that the up-gradient PV fluxes represent local wave decay and are maintained by poleward fluxes of PV variance. Finite-amplitude effects thus represent leading order contributions to the PV variance budget, whereas dissipation is only of secondary importance locally. The appearance of up-gradient PV fluxes in the long-term mean is associated with the poleward shift of the jet—and thus the region of wave decay relative to wave growth—following wave-breaking events.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Transition from suppressed to active convection modulated by a weak-temperature gradient derived large-scale circulation

Numerical simulations are performed to assess the influence of the large-scale circulation on the transition from suppressed to active convection. As a model tool, we used a coupled-column model. It consists of two cloud-resolving models which are fully coupled via a large-scale circulation which is derived from the requirement that the instantaneous domain-mean potential temperature profiles of the two columns remain close to each other. This is known as the weak-temperature gradient approach. The simulations of the transition are initialized from coupled-column simulations over non-uniform surface forcing and the transition is forced within the dry column by changing the local and/or remote surface forcings to uniform surface forcing across the columns. As the strength of the circulation is reduced to zero, moisture is recharged into the dry column and a transition to active convection occurs once the column is sufficiently moistened to sustain deep convection. Direct effects of changing surface forcing occur over the first few days only. Afterward, it is the evolution of the large-scale circulation which systematically modulates the transition. Its contributions are approximately equally divided between the heating and moistening effects. A transition time is defined to summarize the evolution from suppressed to active convection. It is the time when the rain rate within the dry column is halfway to the mean value obtained at equilibrium over uniform surface forcing. The transition time is around twice as long for a transition that is forced remotely compared to a transition that is forced locally. Simulations in which both local and remote surface forcings are changed produce intermediate transition times.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

Environmental controls on the distribution and diversity of lentic Chironomidae (Insecta: Diptera) across an altitudinal gradient in tropical South America

To predict the response of aquatic ecosystems to future global climate change, data on the ecology and distribution of keystone groups in freshwater ecosystems are needed. In contrast to mid- and high-latitude zones, such data are scarce across tropical South America (Neotropics). We present the distribution and diversity of chironomid species using surface sediments of 59 lakes from the Andes to the Amazon (0.1–17°S and 64–78°W) within the Neotropics. We assess the spatial variation in community assemblages and identify the key variables influencing the distributional patterns. The relationships between environmental variables (pH, conductivity, depth, and sediment organic content), climatic data, and chironomid assemblages were assessed using multivariate statistics (detrended correspondence analysis and canonical correspondence analysis). Climatic parameters (temperature and precipitation) were most significant in describing the variance in chironomid assemblages. Temperature and precipitation are both predicted to change under future climate change scenarios in the tropical Andes. Our findings suggest taxa of Orthocladiinae, which show a preference to cold high-elevation oligotrophic lakes, will likely see range contraction under future anthropogenic-induced climate change. Taxa abundant in areas of high precipitation, such as Micropsectra and Phaenopsectra, will likely become restricted to the inner tropical Andes, as the outer tropical Andes become drier. The sensitivity of chironomids to climate parameters makes them important bio-indicators of regional climate change in the Neotropics. Furthermore, the distribution of chironomid taxa presented here is a vital first step toward providing urgently needed autecological data for interpreting fossil chironomid records of past ecological and climate change from the tropical Andes.