Singular and regular solutions of a non-linear parabolic system

We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$. For dimensions $n>4$ we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.Comment: 16 page

Intention of preserving forest remnants among landowners in the Atlantic Forest: The role of the ecological context via ecosystem services

Unravelling the psychological processes determining landowners' support towards forest conservation is crucial, particularly in rural areas of the tropics, where most forest remnants are within private lands. As human–nature connections are known to shape pro‐environmental behaviours, the intention of preserving forest remnants should ultimately be determined by the ecological context people live in. Here, we investigate the pathways through which the ecological context (forest cover), via direct contact with forests and ecosystem services and disservices, influence the psychological antecedents of conservation behaviour (beliefs, attitude and intention of preserving forest remnants). We conceptualized a model based on the Reasoned Action Approach, using the ecological context and these three forest experiences as background factors, and tested the model using Piecewise Structural Equation Modelling. Data were collected through an interview‐based protocol applied to 106 landowners across 13 landscapes varying in forest cover in a consolidated rural region in the Brazilian Atlantic Forest. Our results indicate that: (a) ecosystem services are more important than disservices for shaping intention of preserving forests, particularly non‐provisioning services; (b) contact with forest has an indirect effect on intention, by positively influencing the frequency of receiving ecosystem services; (c) people living in more forested ecological contexts have more contact with forests, receive ecosystem services more frequently and, ultimately, have stronger intention of preserving forests. Hence, our study suggests a dangerous positive feedback loop between deforestation, the extinction of forest experiences and impairment of human–nature connections. Local demands across the full range of ecosystem services, the balance between services and disservices and the ecological context people live in should be considered when developing conservation initiatives in tropical rural areas

Cork derived TiO2 biomorphic ecoceramics

Environmentally conscious biomorphic ceramics (Ecoceramics) are a new class of material manufactured from renewable resources and wastes. Sustainable cork wastes were pyrolysed, and this activated carbon template infiltrated with a sol-gel precursor (from aqueous green-chemistry) to form TiO2 on heating in air, with the honeycomb microstructure of cork. Physical and optical band gap properties were characterised by XRD, SEM and Raman and UV–vis spectroscopy, and differences between alkaline and acidic activation of the carbon template also studied. With activation by HCl, HNO3 or H2SO4, a mixture of anatase and rutile formed. NaOH activation resulted in pure anatase, but a large amount of Na was retained. At 1000 °C acid activated ecoceramics formed pure rutile, but the NaOH activated one formed Na2Ti6O13 (sodium hexatitanate) as the major phase, coexisting with anatase, brookite and rutile. This material is worth further investigation, as Na2Ti6O13 is reported as a photocatalyst in its own right

Local ecosystem feedbacks and critical transitions in the climate

Global and regional climate models, such as those used in IPCC assessments, are the best tools available for climate predictions. Such models typically account for large-scale land-atmosphere feedbacks. However, these models omit local vegetationenvironment 5 feedbacks that are crucial for critical transitions in ecosystems. Here, we reveal the hypothesis that, if the balance of feedbacks is positive at all scales, local vegetation-environment feedbacks may trigger a cascade of amplifying effects, propagating from local to large scale, possibly leading to critical transitions in the largescale climate. We call for linking local ecosystem feedbacks with large-scale land10 atmosphere feedbacks in global and regional climate models in order to yield climate predictions that we are more confident about

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems

We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake ecosystem model by augmenting the individual cognitive maps drawn by 8 scientists working in the area of shallow lake ecology. We calculated graph theoretical indices of the individual cognitive maps and the collective cognitive map produced by augmentation. The graph theoretical indices revealed internal cycles showing non-linear dynamics in the shallow lake ecosystem. The ecological processes were organized democratically without a top-down hierarchical structure. The steady state condition of the generic model was a characteristic turbid shallow lake ecosystem since there were no dynamic environmental changes that could cause shifts between a turbid and a clearwater state, and the generic model indicated that only a dynamic disturbance regime could maintain the clearwater state. The model developed herein captured the empirical behavior of shallow lakes, and contained the basic model of the Alternative Stable States Theory. In addition, our model expanded the basic model by quantifying the relative effects of connections and by extending it. In our expanded model we ran 4 simulations: harvesting submerged plants, nutrient reduction, fish removal without nutrient reduction, and biomanipulation. Only biomanipulation, which included fish removal and nutrient reduction, had the potential to shift the turbid state into clearwater state. The structure and relationships in the generic model as well as the outcomes of the management simulations were supported by actual field studies in shallow lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to understand the complex structure of shallow lake ecosystems as a whole and obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500