Have ozone effects on carbon sequestration been overestimated?: a new biomass response function for wheat

Elevated levels of tropospheric ozone can significantly impair the growth of crops. The reduced removal of CO2 by plants leads to higher atmospheric concentrations of CO2, enhancing radiative forcing. Ozone effects on economic yield, e.g. the grain yield of wheat (Triticum aestivum L.), are currently used to model effects on radiative forcing. However, changes in grain yield do not necessarily reflect changes in total biomass. Based on an analysis of 22 ozone exposure experiments with field-grown wheat, we investigated whether the use of effects on grain yield as a proxy for effects on biomass under- or overestimates effects on biomass. First, we confirmed that effects on partitioning and biomass loss are both of significant importance for wheat yield loss. Then we derived ozone dose response functions for biomass loss and for harvest index (the proportion of above-ground biomass converted to grain) based on 12 experiments and recently developed ozone uptake modelling for wheat. Finally, we used a European-scale chemical transport model (EMEP MSC-West) to assess the effect of ozone on biomass (−9%) and grain yield (−14%) loss over Europe. Based on yield data per grid square, we estimated above-ground biomass losses due to ozone in 2000 in Europe, totalling 22.2 million tonnes. Incorrectly applying the grain yield response function to model effects on biomass instead of the biomass response function of this paper would have indicated total above-ground biomass losses totalling 38.1 million (i.e. overestimating effects by 15.9 million tonnes). A key conclusion from our study is that future assessments of ozone-induced loss of agroecosystem carbon storage should use response functions for biomass, such as that provided in this paper, not grain yield, to avoid overestimation of the indirect radiative forcing from ozone effects on crop biomass accumulation

Avoided intersections of nodal lines

We consider real eigen-functions of the Schr\"odinger operator in 2-d. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains. In contrast, for wave functions of non integrable systems nodal intersections are rare, and for random waves, the expected number of intersections in any finite area vanishes. However, nodal lines display characteristic avoided crossings which we study in the present work. We define a measure for the avoidance range and compute its distribution for the random waves ensemble. We show that the avoidance range distribution of wave functions of chaotic systems follow the expected random wave distributions, whereas for wave functions of classically integrable but quantum non-separable wave functions, the distribution is quite different. Thus, the study of the avoidance distribution provides more support to the conjecture that nodal structures of chaotic systems are reproduced by the predictions of the random waves ensemble.Comment: 12 pages, 4 figure

Nodal domains on quantum graphs

We consider the real eigenfunctions of the Schr\"odinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of bonds $B$. For well connected graphs, with incommensurate bond lengths, the distribution of the number of nodal domains in the interval mentioned above approaches a Gaussian distribution in the limit when the number of vertices is large. The approach to this limit is not simple, and we discuss it in detail. At the same time we define a random wave model for graphs, and compare the predictions of this model with analytic and numerical computations.Comment: 19 pages, uses IOP journal style file

A lower bound for nodal count on discrete and metric graphs

According to a well-know theorem by Sturm, a vibrating string is divided into exactly N nodal intervals by zeros of its N-th eigenfunction. Courant showed that one half of Sturm's theorem for the strings applies to the theory of membranes: N-th eigenfunction cannot have more than N domains. He also gave an example of a eigenfunction high in the spectrum with a minimal number of nodal domains, thus excluding the existence of a non-trivial lower bound. An analogue of Sturm's result for discretizations of the interval was discussed by Gantmacher and Krein. The discretization of an interval is a graph of a simple form, a chain-graph. But what can be said about more complicated graphs? It has been known since the early 90s that the nodal count for a generic eigenfunction of the Schrodinger operator on quantum trees (where each edge is identified with an interval of the real line and some matching conditions are enforced on the vertices) is exact too: zeros of the N-th eigenfunction divide the tree into exactly N subtrees. We discuss two extensions of this result in two directions. One deals with the same continuous Schrodinger operator but on general graphs (i.e. non-trees) and another deals with discrete Schrodinger operator on combinatorial graphs (both trees and non-trees). The result that we derive applies to both types of graphs: the number of nodal domains of the N-th eigenfunction is bounded below by N-L, where L is the number of links that distinguish the graph from a tree (defined as the dimension of the cycle space or the rank of the fundamental group of the graph). We also show that if it the genericity condition is dropped, the nodal count can fall arbitrarily far below the number of the corresponding eigenfunction.Comment: 15 pages, 4 figures; Minor corrections: added 2 important reference

On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions

Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains $\nu_n$ of the $n$-th eigenfunction satisfies $n\ge \nu_n$. Here, we provide a new interpretation for the Courant nodal deficiency $d_n = n-\nu_n$ in the case of quantum graphs. It equals the Morse index --- at a critical point --- of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning --- it is the number of unstable directions in the vicinity of the critical point corresponding to the $n$-th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.Comment: 22 pages, 6 figure

Dynamics of nodal points and the nodal count on a family of quantum graphs

We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schr\"odinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive several formulas relating the number of the zeros of the n-th eigenfunction to the spectrum of the graph and of some of its subgraphs. In a special case of the so-called dihedral graph we prove an explicit formula that only uses the lengths of the edges, entirely bypassing the information about the graph's eigenvalues. The results are explained from the point of view of the dynamics of zeros of the solutions to the scattering problem.Comment: 34 pages, 12 figure

A new fireworm (Amphinomidae) from the Cretaceous of Lebanon identified from three-dimensionally preserved myoanatomy

© 2015 Parry et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. The attached file is the published version of the article

Anatomy of quantum chaotic eigenstates

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result

Policy design for the Anthropocene

This is the author accepted manuscript. The final version is available from Nature Research via the DOI in this recordToday, more than ever, ‘Spaceship Earth’ is an apt metaphor as we chart the boundaries for a safe planet1. Social scientists both analyse why society courts disaster by approaching or even overstepping these boundaries and try to design suitable policies to avoid these perils. Because the threats of transgressing planetary boundaries are global, long-run, uncertain and interconnected, they must be analysed together to avoid conflicts and take advantage of synergies. To obtain policies that are effective at both international and local levels requires careful analysis of the underlying mechanisms across scientific disciplines and approaches, and must take politics into account. In this Perspective, we examine the complexities of designing policies that can keep Earth within the biophysical limits favourable to human life.Stockholm Resilience CentreBECC - Biodiversity and Ecosystem services in a Changing ClimateMistra Carbon Exi