We study the scaling behavior of two-dimensional (2D) crystalline membranes in the flat phase by a renormalization group (RG) method and an ε-expansion. Generalization of the problem to non-integer ...dimensions, necessary to control the ε-expansion, is achieved by dimensional continuation of a well-known effective theory describing out-of-plane fluctuations coupled to phonon-mediated interactions via a scalar composite field, equivalent for small deformations to the local Gaussian curvature. The effective theory, which will be referred to as Gaussian curvature interaction (GCI) model, is equivalent to theories of elastic D-dimensional manifolds fluctuating in a (D+dc)-dimensional embedding space in the physical case D=2 for arbitrary dc. For D≠2, instead, the GCI model is not equivalent to a direct dimensional continuation of elastic membrane theory and it defines an alternative generalization to generic internal dimension D. After decoupling interactions through a Hubbard-Stratonovich transformation, we study the GCI model by perturbative field-theoretic RG within the framework of an expansion in ε=(4−D). We calculate explicitly RG functions at two-loop order and determine the exponent η characterizing the long-wavelength scaling of correlation functions to order ε2. The value of η at this order is shown to be insensitive to Feynman diagrams involving vertex corrections. As a consequence, the self-consistent screening approximation for the GCI model is shown to be exact to O(ε2). In the physical case of a single out-of-plane displacement field, dc=1, the O(ε2) correction is suppressed by a small numerical prefactor. As a result, despite the large value of ε=2, extrapolation of the first and second order results to D=2 leads to very close numbers, η=0.8 and η≃0.795. The calculated exponent values are close to earlier reference results obtained by non-perturbative renormalization group, the self-consistent screening approximation and numerical simulations. These indications suggest that a perturbative analysis of the GCI model could provide an useful framework for accurate quantitative predictions of the scaling exponent even at D=2.
We investigate the relation between dilatation and conformal symmetries in the statistical mechanics of flexible crystalline membranes. We analyze, in particular, a well-known model which describes ...the fluctuations of a continuum elastic medium embedded in a higher-dimensional space. In this theory, the renormalization group flow connects a non-interacting ultraviolet fixed point, where the theory is controlled by linear elasticity, to an interacting infrared fixed point. By studying the structure of correlation functions and of the energy-momentum tensor, we show that, in the infrared, the theory is only scale-invariant: the dilatation symmetry is not enhanced to full conformal invariance. The model is shown to present a non-vanishing virial current which, despite being non-conserved, maintains a scaling dimension exactly equal to D−1, even in presence of interactions. We attribute the absence of anomalous dimensions to the symmetries of the model under translations and rotations in the embedding space, which are realized as shifts of phonon fields, and which protect the renormalization of several non-invariant operators. We also note that closure of a symmetry algebra with both shift symmetries and conformal invariance would require, in the hypothesis that phonons transform as primary fields, the presence of new shift symmetries which are not expected to hold on physical grounds. We then consider an alternative model, involving only scalar fields, which describes effective phonon-mediated interactions between local Gaussian curvatures. The model is described in the ultraviolet by two copies of the biharmonic theory, which is conformal, but flows in the infrared to a fixed point which we argue to be only dilatation-invariant.
Forest disturbance regimes are expected to intensify as Earth's climate changes. Quantifying forest vulnerability to disturbances and understanding the underlying mechanisms is crucial to develop ...mitigation and adaptation strategies. However, observational evidence is largely missing at regional to continental scales. Here, we quantify the vulnerability of European forests to fires, windthrows and insect outbreaks during the period 1979-2018 by integrating machine learning with disturbance data and satellite products. We show that about 33.4 billion tonnes of forest biomass could be seriously affected by these disturbances, with higher relative losses when exposed to windthrows (40%) and fires (34%) compared to insect outbreaks (26%). The spatial pattern in vulnerability is strongly controlled by the interplay between forest characteristics and background climate. Hotspot regions for vulnerability are located at the borders of the climate envelope, in both southern and northern Europe. There is a clear trend in overall forest vulnerability that is driven by a warming-induced reduction in plant defence mechanisms to insect outbreaks, especially at high latitudes.
We present EU-Forest, a dataset that integrates and extends by almost one order of magnitude the publicly available information on European tree species distribution. The core of our dataset (~96% of ...the occurrence records) came from an unpublished, large database harmonising forest plot surveys from National Forest Inventories on an INSPIRE-compliant 1 km×1 km grid. These new data can potentially benefit several disciplines, including forestry, biodiversity conservation, palaeoecology, plant ecology, the bioeconomy, and pest management.
We present "EU-Trees4F", a dataset of current and future potential distributions of 67 tree species in Europe at 10 km spatial resolution. We provide both climatically suitable future areas of ...occupancy and the future distribution expected under a scenario of natural dispersal for two emission scenarios (RCP 4.5 and RCP 8.5) and three time steps (2035, 2065, and 2095). Also, we provide a version of the dataset where tree ranges are limited by future land use. These data-driven projections were made using an ensemble species distribution model calibrated using EU-Forest, a comprehensive dataset of tree species occurrences for Europe, and driven by seven bioclimatic parameters derived from EURO-CORDEX regional climate model simulations, and two soil parameters. "EU-Trees4F", can benefit various research fields, including forestry, biodiversity, ecosystem services, and bio-economy. Possible applications include the calibration or benchmarking of dynamic vegetation models, or informing forest adaptation strategies based on assisted tree migration. Given the multiple European policy initiatives related to forests, this dataset represents a timely and valuable resource to support policymaking.
The alpine tundra is the highest elevation belt of high mountains. This zone is an important reservoir of freshwater and provides habitat to unique species. This study assesses projected changes in ...the areal extent of the alpine tundra climate zone in three warming levels in European mountains. The alpine tundra was delineated using the Köppen-Geiger climate classification. We used 11 regional climate model simulations from EURO-CORDEX disaggregated at a one-kilometre grid size representing the RCP4.5 and RCP8.5 scenarios in the 1.5, 2 and 3 °C warming levels. Mitigation represented by the 1.5 °C warming level reduces projected losses of the alpine tundra. However, even in this warming level the projected contraction is severe. In this case, the contraction in the Alps, Scandes and Pyrenees together is projected at between 44% and 48% of the present extent. The contraction is projected to climb in the 2 °C warming to above 57%, while the 3 °C warming would imply that the alpine tundra will be near to collapse in Europe with a contraction of 84% in the three regions, which host most of the alpine tundra in Europe. The projected changes have negative implications for a range of ecosystem services and biodiversity, such as habitat provision, water provision and regulation, erosion protection, water quality and recreational services.
Contemporaneous plant communities may retain a mark of past disturbances in their ecological patterns. However, unraveling the history of disturbance on natural systems at a large scale is often ...unfeasible, due to the complexity of the factors involved and lack of historical data. Here we aim at demonstrating how comparing observed spatial structure of tree assemblages with that expected in a hypothetical, undisturbed scenario can shed light on how natural European forests are. Borrowing an analytical approach developed in the field of network analysis, we assessed how much the observed ecological patterns of nestedness (i.e. positive co-occurrence), segregation (i.e. negative co-occurrence), and modularity in tree assemblages deviate from randomness, and from those projected by Potential Natural Vegetation (PNV) geobotanical expert assessments. We found clear evidence that European forests are far from a natural condition, showing only moderate signals (especially at higher latitudes) of the ecological spatial structure typical of undisturbed vegetation (i.e. nestedness). Our results highlight how taking into account spatial structure along with diversity can be a fundamental tool to address this problem and assess the degree of naturalness in species assemblages.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Luttinger semimetals are three-dimensional electron systems with a parabolic band touching and an effective total spin J=3/2. In this paper, we present an analytical theory of dielectric screening of ...inversion-symmetric Luttinger semimetals with an arbitrary carrier density and conduction-valence effective mass asymmetry. Assuming a spherical approximation for the single-particle Luttinger Hamiltonian, we determine analytically the dielectric screening function in the random phase approximation for arbitrary values of the wave vector and frequency, the latter in the complex plane. We use this analytical expression to calculate the dispersion relation and Landau damping of the collective modes in the charge sector (i.e., plasmons).
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