A Numerical Study of the 2-Flavour Schwinger Model with Dynamical Overlap Hypercube Fermions

We present numerical results for the 2-flavour Schwinger model with dynamical chiral lattice fermions. We insert an approximately chiral hypercube Dirac operator into the overlap formula to construct the overlap hypercube operator. This is an exact solution to the Ginsparg-Wilson relation, with an excellent level of locality and scaling. Due to its similarity with the hypercubic kernel, a low polynomial in this kernel provides a numerically efficient Hybrid Monte Carlo force. We measure the microscopic Dirac spectrum and discuss the corresponding scale-invariant parameter, which takes a surprising form. This is an interesting case, since Random Matrix Theory is unexplored for this setting, where the chiral condensate {\Sigma} vanishes in the chiral limit. We also measure {\Sigma} and the "pion" mass, in distinct topological sectors. In this context we discuss and probe the topological summation of observables by various methods, as well as the evaluation of the topological susceptibility. The feasibility of this summation is essential for the prospects of dynamical overlap fermions in QCD.Comment: 44 pages, LaTex, 12 tables, 17 figures, final version published in Eur. Phys. J.

A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability

Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter $\theta$, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on $\theta$ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.Comment: 29 pages, 23 figures, references adde

Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/\theta Expansion

We analyze the $1/\theta$ and 1/N expansions of the Wilson loop averages $_{U_\theta (N)}$ in the two-dimensional noncommutative $U_\theta (N)$ gauge theory with the parameter of noncommutativity $\theta$. For a generic rectangular contour $C$, a concise integral representation is derived (non-perturbatively both in the coupling constant $g^{2}$ and in $\theta$) for the next-to-leading term of the $1/\theta$ expansion. In turn, in the limit when ${\theta}$ is much larger than the area $A(C)$ of the surface bounded by $C$, the large $\theta$ asymptote of this representation is argued to yield the next-to-leading term of the $1/\theta$ series. For both of the expansions, the next-to-leading contribution exhibits only a power-like decay for areas $A(C)>>\sigma^{-1}$ (but $A(C)<<{\theta}$) much larger than the inverse of the string tension $\sigma$ defining the range of the exponential decay of the leading term. Consequently, for large $\theta$, it hinders a direct stringy interpretation of the subleading terms of the 1/N expansion in the spirit of Gross-Taylor proposal for the $\theta=0$ commutative D=2 gauge theory.Comment: LaTex, 50pp., 9 PostScript figure

Accuracy, realism and general applicability of European forest models

Forest models are instrumental for understanding and projecting the impact of climate change on forests. A considerable number of forest models have been developed in the last decades. However, few systematic and comprehensive model comparisons have been performed in Europe that combine an evaluation of modelled carbon and water fluxes and forest structure. We evaluate 13 widely used, state-of-the-art, stand-scale forest models against field measurements of forest structure and eddy-covariance data of carbon and water fluxes over multiple decades across an environmental gradient at nine typical European forest stands. We test the models\u27 performance in three dimensions: accuracy of local predictions (agreement of modelled and observed annual data), realism of environmental responses (agreement of modelled and observed responses of daily gross primary productivity to temperature, radiation and vapour pressure deficit) and general applicability (proportion of European tree species covered). We find that multiple models are available that excel according to our three dimensions of model performance. For the accuracy of local predictions, variables related to forest structure have lower random and systematic errors than annual carbon and water flux variables. Moreover, the multi-model ensemble mean provided overall more realistic daily productivity responses to environmental drivers across all sites than any single individual model. The general applicability of the models is high, as almost all models are currently able to cover Europe\u27s common tree species. We show that forest models complement each other in their response to environmental drivers and that there are several cases in which individual models outperform the model ensemble. Our framework provides a first step to capturing essential differences between forest models that go beyond the most commonly used accuracy of predictions. Overall, this study provides a point of reference for future model work aimed at predicting climate impacts and supporting climate mitigation and adaptation measures in forests

Local Difference Measures between Complex Networks for Dynamical System Model Evaluation

Acknowledgments We thank Reik V. Donner for inspiring suggestions that initialized the work presented herein. Jan H. Feldhoff is credited for providing us with the STARS simulation data and for his contributions to fruitful discussions. Comments by the anonymous reviewers are gratefully acknowledged as they led to substantial improvements of the manuscript.Peer reviewedPublisher PD

Accuracy, realism and general applicability of European forest models

Forest models are instrumental for understanding and projecting the impact of climate change on forests. A considerable number of forest models have been developed in the last decades. However, few systematic and comprehensive model comparisons have been performed in Europe that combine an evaluation of modelled carbon and water fluxes and forest structure. We evaluate 13 widely used, state-of-the-art, stand-scale forest models against field measurements of forest structure and eddy-covariance data of carbon and water fluxes over multiple decades across an environmental gradient at nine typical European forest stands. We test the models' performance in three dimensions: accuracy of local predictions (agreement of modelled and observed annual data), realism of environmental responses (agreement of modelled and observed responses of daily gross primary productivity to temperature, radiation and vapour pressure deficit) and general applicability (proportion of European tree species covered). We find that multiple models are available that excel according to our three dimensions of model performance. For the accuracy of local predictions, variables related to forest structure have lower random and systematic errors than annual carbon and water flux variables. Moreover, the multi-model ensemble mean provided overall more realistic daily productivity responses to environmental drivers across all sites than any single individual model. The general applicability of the models is high, as almost all models are currently able to cover Europe's common tree species. We show that forest models complement each other in their response to environmental drivers and that there are several cases in which individual models outperform the model ensemble. Our framework provides a first step to capturing essential differences between forest models that go beyond the most commonly used accuracy of predictions. Overall, this study provides a point of reference for future model work aimed at predicting climate impacts and supporting climate mitigation and adaptation measures in forests.Peer reviewe

Global ensemble projections reveal trophic amplification of ocean biomass declines with climate change

While the physical dimensions of climate change are now routinely assessed through multimodel intercomparisons, projected impacts on the global ocean ecosystem generally rely on individual models with a specific set of assumptions. To address these single-model limitations, we present standardized ensemble projections from six global marine ecosystem models forced with two Earth system models and four emission scenarios with and without fishing. We derive average biomass trends and associated uncertainties across the marine food web. Without fishing, mean global animal biomass decreased by 5% (±4% SD) under low emissions and 17% (±11% SD) under high emissions by 2100, with an average 5% decline for every 1 °C of warming. Projected biomass declines were primarily driven by increasing temperature and decreasing primary production, and were more pronounced at higher trophic levels, a process known as trophic amplification. Fishing did not substantially alter the effects of climate change. Considerable regional variation featured strong biomass increases at high latitudes and decreases at middle to low latitudes, with good model agreement on the direction of change but variable magnitude. Uncertainties due to variations in marine ecosystem and Earth system models were similar. Ensemble projections performed well compared with empirical data, emphasizing the benefits of multimodel inference to project future outcomes. Our results indicate that global ocean animal biomass consistently declines with climate change, and that these impacts are amplified at higher trophic levels. Next steps for model development include dynamic scenarios of fishing, cumulative human impacts, and the effects of management measures on future ocean biomass trends

The PROFOUND Database for evaluating vegetation models and simulating climate impacts on European forests

Process-based vegetation models are widely used to predict local and global ecosystem dynamics and climate change impacts. Due to their complexity, they require careful parameterization and evaluation to ensure that projections are accurate and reliable. The PROFOUND Database (PROFOUND DB) provides a wide range of empirical data on European forests to calibrate and evaluate vegetation models that simulate climate impacts at the forest stand scale. A particular advantage of this database is its wide coverage of multiple data sources at different hierarchical and temporal scales, together with environmental driving data as well as the latest climate scenarios. Specifically, the PROFOUND DB provides general site descriptions, soil, climate, CO2, nitrogen deposition, tree and forest stand level, and remote sensing data for nine contrasting forest stands distributed across Europe. Moreover, for a subset of five sites, time series of carbon fluxes, atmospheric heat conduction and soil water are also available. The climate and nitrogen deposition data contain several datasets for the historic period and a wide range of future climate change scenarios following the Representative Concentration Pathways (RCP2.6, RCP4.5, RCP6.0, RCP8.5). We also provide pre-industrial climate simulations that allow for model runs aimed at disentangling the contribution of climate change to observed forest productivity changes. The PROFOUND DB is available freely as a "SQLite" relational database or "ASCII" flat file version (at https://doi.org/10.5880/PIK.2020.006/; Reyer et al., 2020). The data policies of the individual contributing datasets are provided in the metadata of each data file. The PROFOUND DB can also be accessed via the ProfoundData R package (https://CRAN.R- project.org/package=ProfoundData; Silveyra Gonzalez et al., 2020), which provides basic functions to explore, plot and extract the data for model set-up, calibration and evaluation.Peer reviewe

Complex networks for climate model evaluation with application to statistical versus dynamical modeling of South American climate

Acknowledgments: This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. Furthermore, this work has been financially supported by the Leibniz Society (project ECONS), and the Stordalen Foundation (JFD). For certain calculations, the software packages pyunicorn (Donges et al. 2013a) and igraph (Csa´rdi and Nepusz 2006) were used. The authors would like to thank Manoel F. Cardoso, Niklas Boers, and the reviewers for helpful comments on the manuscript. Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Peer reviewedPostprin