Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Bailouts in a common market: a strategic approach

Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm

The New Political Economy of EU State Aid Policy

Despite its importance and singularity, the EU’s state aid policy has attracted less scholarly attention than other elements of EU competition policy. Introducing the themes addressed by the special issue, this article briefly reviews the development of EU policy and highlights why the control of state aid matters. The Commission’s response to the current economic crisis notably in banking and the car industry is a key concern, but the interests of the special issue go far beyond. They include: the role of the European Commission in the development of EU policy, the politics of state aid, and a clash between models of capitalism. The special issue also examines the impact of EU policy. It investigates how EU state aid decisions affect not only industrial policy at the national level (and therefore at the EU level), but the welfare state and territorial relations within federal member states, the external implications of EU action and the strategies pursued by the Commission to limit any potential disadvantage to European firms, and the conflict between the EU’s expanding legal order and national

Critical gaps in nanoplastics research and their connection to risk assessment

Reports of plastics, at higher levels than previously thought, in the water that we drink and the air that we breathe, are generating considerable interest and concern. Plastics have been recorded in almost every environment in the world with estimates on the order of trillions of microplastic pieces. Yet, this may very well be an underestimate of plastic pollution as a whole. Once microplastics (<5 mm) break down in the environment, they nominally enter the nanoscale (<1,000 nm), where they cannot be seen by the naked eye or even with the use of a typical laboratory microscope. Thus far, research has focused on plastics in the macro- (>25 mm) and micro-size ranges, which are easier to detect and identify, leaving large knowledge gaps in our understanding of nanoplastic debris. Our ability to ask and answer questions relating to the transport, fate, and potential toxicity of these particles is disadvantaged by the detection and identification limits of current technology. Furthermore, laboratory exposures have been substantially constrained to the study of commercially available nanoplastics; i.e., polystyrene spheres, which do not adequately reflect the composition of environmental plastic debris. While a great deal of plastic-focused research has been published in recent years, the pattern of the work does not answer a number of key factors vital to calculating risk that takes into account the smallest plastic particles; namely, sources, fate and transport, exposure measures, toxicity and effects. These data are critical to inform regulatory decision making and to implement adaptive management strategies that mitigate risk to human health and the environment. This paper reviews the current state-of-the-science on nanoplastic research, highlighting areas where data are needed to establish robust risk assessments that take into account plastics pollution. Where nanoplastic-specific data are not available, suggested substitutions are indicated

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Supernova 1987A: Rotation and a Binary Companion

In this paper we provide a possible link between the structure of the bipolar nebula surrounding SN1987A and the properties of its progenitor star. A Wind Blwon Bubble (WBB) scenario is emplyed, in which a fast, tenuous wind from a Blue Supergiant expands into a slow, dense wind, expelled during an earlier Red Supergiant phase. The bipolar shapre develops due to a pole-to-equator density contrast in the slow wind (ie, the slow wind forms a slow torus). We use the Wind Compressed Disk (WCD) model of Bjorkman & Cassinelli (1992) to determine the shape of the slow torus. In the WCD scenario, the shape of the torus is determined by the rotation of the progenitor star. We then use a self-similar semi-analytical method for wind blown bubble evolution to determine the shape of the resulting bipolar nebula. We find that the union of the wind-compressed-disk and bipolar-wind-blown- bubble models allows us to recover the salient properties of SN1987A's circumstellar nebula. In particular, the size, speed and density of SN1987A's inner ring are easily reproduced in our calculations. An exploration of parameter space shows the the red supergiant progenitor must be been rotating at > 0.3 of its breakup speed. We conclude that the progenitor was most likely spun up by a merger with a binary companion. Using a simple model for the binary merger we find that the companion is likely to have had a mass > 0.5 M_sun.Comment: 30 pages, 4 figure

Scattering from Singular Potentials in Quantum Mechanics

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r variable. The present paper extends those early results to an arbitrary number of spatial dimensions. The Hill-type equation which leads, in principle, to the evaluation of the polydromy parameter, is obtained from the Hill equation for a two-dimensional problem by means of a simple change of variables. The asymptotic forms of the wave function as r tends to zero and as r tends to infinity are also derived. The Darboux technique of intertwining operators is then applied to obtain an algorithm that makes it possible to solve the Schrodinger equation with a singular potential containing many negative powers of r, if the exact solution with even just one term is already known.Comment: 19 pages, plain Tex. In this revised version, the analysis of Eq. (5.29) has been amended, and an appendix has been added for completenes

Mapping the economic value of landslide regulation by forests

The role of forests in regulating landslide risks is well established but estimates of the economic value of this ecosystem service are limited. In order to incorporate the role of forests for landslide risk mitigation in spatial planning and other decision-making contexts, there is a need for spatially explicit information regarding the value of this service. We develop a methodological framework to combine bio-physical modelling of natural hazard risk and socio-economic exposure in a predictive model to estimate and map of the economic value of forest regulation of landslides. This method is applied in a case study of Adjara Autonomous Republic of Georgia to examine alternative scenarios for forest management and associated land cover change. The approach produces credible spatially explicit results to inform policy decisions regarding investment in forest management; and has the potential for replication in other data scarce regions

Economic values for ecosystem services:A global synthesis and way forward

This paper presents a global synthesis of economic values for ecosystem services provided by 15 terrestrial and marine biomes. Information from over 1,300 studies, yielding over 9,400 value estimates in monetary units, has been collected and organised in the Ecosystem Services Valuation Database (ESVD). This is a substantial expansion of data since the de Groot et al. (2012) description of the ESVD and provides an important juncture to explore developments in the use of valuation methods and the contexts in which valuations are conducted. In this paper we provide summary values for 23 ecosystem services from 15 biomes to represent the magnitude, variation and gaps in economic values. To enable the comparison and synthesis of values, estimates in the ESVD are standardised to a common set of units (Int$/ha/year at 2020 price levels). This data provides a basis for value transfers to inform decision-making in current policy contexts but requires due consideration and adjustment for context specific determinants of value. Although the coverage of the ESVD is global, the geographic distribution of data is not even. There is a particularly high representation of European ecosystems and relatively little information for Russia, Central Asia and North Africa. Therefore, the data are not globally representative of biophysical and socio-economic contexts. The distribution of data across ecosystem services is also far from even, with some services very well represented (e.g. recreation, wild fish and wild animals, ecosystem and species appreciation, air filtration and global climate regulation) and others with almost no value estimates (e.g. disease control, water baseflow maintenance, rainfall pattern regulation). In the past decade, there has been a notable increase in demand for information on the economic value of ecosystem services from both public and private institutions to improve the conservation and management of natural capital. The literature is developing to meet this demand but there is a need for targeted and refined valuation research to ensure sufficient certainty, comparability, and representativeness of the data, and to enable transferability and fill knowledge gaps. This paper concludes by identifying avenues for future development to further increase the amount, quality, representativeness and application of data on economic values for ecosystem services.</p