Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.Comment: 31 page

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Analysis of laser radiation using the Nonlinear Fourier transform

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions

Dual clumped isotope thermometry resolves kinetic biases in carbonate formation temperatures

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Bajnai, D., Guo, W., Spötl, C., Coplen, T. B., Methner, K., Löffler, N., Krsnik, E., Gischler, E., Hansen, M., Henkel, D., Price, G. D., Raddatz, J., Scholz, D., & Fiebig, J. Dual clumped isotope thermometry resolves kinetic biases in carbonate formation temperatures. Nature Communications, 11(1), (2020): 4005, doi:10.1038/s41467-020-17501-0.Surface temperature is a fundamental parameter of Earth’s climate. Its evolution through time is commonly reconstructed using the oxygen isotope and the clumped isotope compositions of carbonate archives. However, reaction kinetics involved in the precipitation of carbonates can introduce inaccuracies in the derived temperatures. Here, we show that dual clumped isotope analyses, i.e., simultaneous ∆47 and ∆48 measurements on the single carbonate phase, can identify the origin and quantify the extent of these kinetic biases. Our results verify theoretical predictions and evidence that the isotopic disequilibrium commonly observed in speleothems and scleractinian coral skeletons is inherited from the dissolved inorganic carbon pool of their parent solutions. Further, we show that dual clumped isotope thermometry can achieve reliable palaeotemperature reconstructions, devoid of kinetic bias. Analysis of a belemnite rostrum implies that it precipitated near isotopic equilibrium and confirms the warmer-than-present temperatures during the Early Cretaceous at southern high latitudes.This work became possible through DFG grant “INST 161/871-1” and the Investment in Science Fund at Woods Hole Oceanographic Institution. The authors would like to thank Sven Hofmann and Manuel Schumann for their assistance in the joint Goethe University – Senckenberg BiK-F Stable Isotope Facility at the Institute of Geosciences, Goethe University Frankfurt. K.M. acknowledges funding through “DFG ME 4955/1-1”, E.K. through “DFG MU 2845/6-1”, D.S. through “DFG SCHO 1274/8-1” and “DFG SCHO 1274/11-1”, and M.H. through “DFG HA 8694/1-1”. C.S. acknowledges funding from the University of Innsbruck. A review of the manuscript by David Evans on behalf of the USGS is acknowledged

Genetic Differentiation, Structure, and a Transition Zone among Populations of the Pitcher Plant Moth Exyra semicrocea: Implications for Conservation

Pitcher plant bogs, or carnivorous plant wetlands, have experienced extensive habitat loss and fragmentation throughout the southeastern United States Coastal Plain, resulting in an estimated reduction to <3% of their former range. This situation has lead to increased management attention of these habitats and their carnivorous plant species. However, conservation priorities focus primarily on the plants since little information currently exists on other community members, such as their endemic arthropod biota. Here, we investigated the population structure of one of these, the obligate pitcher plant moth Exyra semicrocea (Lepidoptera: Noctuidae), using mitochondrial cytochrome c oxidase subunit I (COI) gene sequences. Examination of 221 individuals from 11 populations across eight southeastern US states identified 51 unique haplotypes. These haplotypes belonged to one of two divergent (∼1.9–3.0%) lineages separated by the Mississippi alluvial plain. Populations of the West Gulf Coastal Plain exhibited significant genetic structure, contrasting with similarly distanced populations east of the Mississippi alluvial plain. In the eastern portion of the Coastal Plain, an apparent transition zone exists between two regionally distinct population groups, with a well-established genetic discontinuity for other organisms coinciding with this zone. The structure of E. semicrocea appears to have been influenced by patchy pitcher plant bog habitats in the West Gulf Coastal Plain as well as impacts of Pleistocene interglacials on the Apalachicola-Chattahoochee-Flint River Basin. These findings, along with potential extirpation of E. semicrocea at four visited, but isolated, sites highlight the need to consider other endemic or associated community members when managing and restoring pitcher plant bog habitats

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe