Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Temperature dependence of binary and ternary recombination of H3+ ions with electron

We study binary and the recently discovered process of ternary He-assisted recombination of H3+ ions with electrons in a low temperature afterglow plasma. The experiments are carried out over a broad range of pressures and temperatures of an afterglow plasma in a helium buffer gas. Binary and He-assisted ternary recombination are observed and the corresponding recombination rate coefficients are extracted for temperatures from 77 K to 330 K. We describe the observed ternary recombination as a two-step mechanism: First, a rotationally-excited long-lived neutral molecule H3* is formed in electron-H3+ collisions. Second, the H3* molecule collides with a helium atom that leads to the formation of a very long-lived Rydberg state with high orbital momentum. We present calculations of the lifetimes of H3* and of the ternary recombination rate coefficients for para and ortho-H3+. The calculations show a large difference between the ternary recombination rate coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured binary and ternary rate coefficients are in reasonable agreement with the calculated values.Comment: 15 page

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Improved Constraints on Sterile Neutrino Mixing from Disappearance Searches in the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments.

Searches for electron antineutrino, muon neutrino, and muon antineutrino disappearance driven by sterile neutrino mixing have been carried out by the Daya Bay and MINOS+ collaborations. This Letter presents the combined results of these searches, along with exclusion results from the Bugey-3 reactor experiment, framed in a minimally extended four-neutrino scenario. Significantly improved constraints on the θ_{μe} mixing angle are derived that constitute the most constraining limits to date over five orders of magnitude in the mass-squared splitting Δm_{41}^{2}, excluding the 90% C.L. sterile-neutrino parameter space allowed by the LSND and MiniBooNE observations at 90% CL_{s} for Δm_{41}^{2}<13  eV^{2}. Furthermore, the LSND and MiniBooNE 99% C.L. allowed regions are excluded at 99% CL_{s} for Δm_{41}^{2}<1.6 eV^{2}

Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes

We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re

The enhanced X-ray Timing and Polarimetry mission – eXTP: an update on its scientific cases, mission profile and development status

The enhanced X-ray Timing and Polarimetry mission (eXTP) is a flagship observatory for X-ray timing, spectroscopy and polarimetry developed by an International Consortium. Thanks to its very large collecting area, good spectral resolution and unprecedented polarimetry capabilities, eXTP will explore the properties of matter and the propagation of light in the most extreme conditions found in the Universe. eXTP will, in addition, be a powerful X-ray observatory. The mission will continuously monitor the X-ray sky, and will enable multiwavelength and multi-messenger studies. The mission is currently in phase B, which will be completed in the middle of 2022

Global transpiration data from sap flow measurements: The SAPFLUXNET database

Plant transpiration links physiological responses of vegetation to water supply and demand with hydrological, energy, and carbon budgets at the land-atmosphere interface. However, despite being the main land evaporative flux at the global scale, transpiration and its response to environmental drivers are currently not well constrained by observations. Here we introduce the first global compilation of whole-plant transpiration data from sap flow measurements (SAPFLUXNET, https://sapfluxnet.creaf.cat/, last access: 8 June 2021). We harmonized and quality-controlled individual datasets supplied by contributors worldwide in a semi-automatic data workflow implemented in the R programming language. Datasets include sub-daily time series of sap flow and hydrometeorological drivers for one or more growing seasons, as well as metadata on the stand characteristics, plant attributes, and technical details of the measurements. SAPFLUXNET contains 202 globally distributed datasets with sap flow time series for 2714 plants, mostly trees, of 174 species. SAPFLUXNET has a broad bioclimatic coverage, with woodland/shrubland and temperate forest biomes especially well represented (80% of the datasets). The measurements cover a wide variety of stand structural characteristics and plant sizes. The datasets encompass the period between 1995 and 2018, with 50% of the datasets being at least 3 years long. Accompanying radiation and vapour pressure deficit data are available for most of the datasets, while on-site soil water content is available for 56% of the datasets. Many datasets contain data for species that make up 90% or more of the total stand basal area, allowing the estimation of stand transpiration in diverse ecological settings. SAPFLUXNET adds to existing plant trait datasets, ecosystem flux networks, and remote sensing products to help increase our understanding of plant water use, plant responses to drought, and ecohydrological processes. SAPFLUXNET version 0.1.5 is freely available from the Zenodo repository (10.5281/zenodo.3971689; Poyatos et al., 2020a). The "sapfluxnetr"R package-designed to access, visualize, and process SAPFLUXNET data-is available from CRAN. © 2021 Rafael Poyatos et al.This research was supported by the Minis-terio de Economía y Competitividad (grant no. CGL2014-55883-JIN), the Ministerio de Ciencia e Innovación (grant no. RTI2018-095297-J-I00), the Ministerio de Ciencia e Innovación (grant no. CAS16/00207), the Agència de Gestió d’Ajuts Universitaris i de Recerca (grant no. SGR1001), the Alexander von Humboldt-Stiftung (Humboldt Research Fellowship for Experienced Researchers (RP)), and the Institució Catalana de Recerca i Estudis Avançats (Academia Award (JMV)). Víctor Flo was supported by the doctoral fellowship FPU15/03939 (MECD, Spain)