Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Persistent acceleration in global sea-level rise since the 1960s

Previous studies reconstructed twentieth-century global mean sea level (GMSL) from sparse tide-gauge records to understand whether the recent high rates obtained from satellite altimetry are part of a longer-term acceleration. However, these analyses used techniques that can only accurately capture either the trend or the variability in GMSL, but not both. Here we present an improved hybrid sea-level reconstruction during 1900–2015 that combines previous techniques at time scales where they perform best. We find a persistent acceleration in GMSL since the 1960s and demonstrate that this is largely (~76%) associated with sea-level changes in the Indo-Pacific and South Atlantic. We show that the initiation of the acceleration in the 1960s is tightly linked to an intensification and a basin-scale equatorward shift of Southern Hemispheric westerlies, leading to increased ocean heat uptake, and hence greater rates of GMSL rise, through changes in the circulation of the Southern Ocean

Uncertainties in steric sea level change estimation during the satellite altimeter era: concepts and practices

This article presents a review of current practice in estimating steric sea level change, focussed on the treatment of uncertainty. Steric sea level change is the contribution to the change in sea level arising from the dependence of density on temperature and salinity. It is a significant component of sea level rise and a reflection of changing ocean heat content. However tracking these steric changes remains still a significant challenge for the scientific community. We review the importance of understanding the uncertainty in estimates of steric sea level change. Relevant concepts of uncertainty are discussed and illustrated with the example of observational uncertainty propagation from a single profile of temperature and salinity measurements to steric height. We summarise and discuss the recent literature on methodologies and techniques used to estimate steric sea level in the context of the treatment of uncertainty. Our conclusions are that progress in quantifying steric sea level uncertainty will benefit from: greater clarity and transparency in published discussions of uncertainty, including exploitation of international standards for quantifying and expressing uncertainty in measurement; and the development of community ‘recipes’ for quantifying the error covariances in observations and from sparse sampling, and for estimating and propagating uncertainty across spatio-temporal scales

The Sea Level Budget Since 2003: Inference on the Deep Ocean Heat Content

International audienceThis study provides an overview of the various components of the global mean sea level evolution over two time spans: (1) 2005–2012 (corresponding to the full deployment of the Argo program) and (2) 2003–2012. Using a sea level budget approach, we compare altimetry-based global mean sea level, global ocean mass from GRACE space gravimetry and steric sea level from Argo and other in situ measurements. One goal of this study is to investigate whether it is possible to constrain the deep ocean contribution to the global mean sea level rise over the last decade. This question is particularly relevant, considering the current debate about the ‘hiatus,’ i.e., the observed recent pause of the global mean air and sea surface temperature evolution while the planet is still in thermal imbalance. We consider a total of 16 different data sets. Differences are noticed between data sets related to each variable (sea level, ocean mass and steric sea level), mostly due to data processing issues. Therefore, we perform the analysis using averages of the available data sets. For each period, we find that, when removing from the global mean sea level, the contributions of the global mean ocean mass and steric sea level (estimated for the 0–1,500 m ocean layer), there remains a residual signal displaying a positive slope of 0.3 ± 0.6 and 0.55 ± 0.6 mm/year over 2005–2012 and 2003–2012, respectively. Comparing with an ocean reanalysis and according to direct (but sparse) ocean temperature measurements below 1,500 m, it seems unlikely that the observed residual signal can be attributed to deep (below 1,500 m) ocean warming, in agreement with other recently published results. We estimate that it possibly reflects, at least partly, the signature of a missing upper ocean steric signal in regions uncovered by current observing systems. Our study also shows a steady warming increase since 2003 of the 700–1,500 m ocean layer (amounting ~0.2 mm/year in steric sea level equivalent), confirming previous findings, but seen in our study in each of the eight different steric data sets considered

Group II Intron-Based Gene Targeting Reactions in Eukaryotes

Mobile group II introns insert site-specifically into DNA target sites by a mechanism termed retrohoming in which the excised intron RNA reverse splices into a DNA strand and is reverse transcribed by the intron-encoded protein. Retrohoming is mediated by a ribonucleoprotein particle that contains the intron-encoded protein and excised intron RNA, with target specificity determined largely by base pairing of the intron RNA to the DNA target sequence. This feature enabled the development of mobile group II introns into bacterial gene targeting vectors ("targetrons") with programmable target specificity. Thus far, however, efficient group II intron-based gene targeting reactions have not been demonstrated in eukaryotes.By using a plasmid-based Xenopus laevis oocyte microinjection assay, we show that group II intron RNPs can integrate efficiently into target DNAs in a eukaryotic nucleus, but the reaction is limited by low Mg(2+) concentrations. By supplying additional Mg(2+), site-specific integration occurs in up to 38% of plasmid target sites. The integration products isolated from X. laevis nuclei are sensitive to restriction enzymes specific for double-stranded DNA, indicating second-strand synthesis via host enzymes. We also show that group II intron RNPs containing either lariat or linear intron RNA can introduce a double-strand break into a plasmid target site, thereby stimulating homologous recombination with a co-transformed DNA fragment at frequencies up to 4.8% of target sites. Chromatinization of the target DNA inhibits both types of targeting reactions, presumably by impeding RNP access. However, by using similar RNP microinjection methods, we show efficient Mg(2+)-dependent group II intron integration into plasmid target sites in zebrafish (Danio rerio) embryos and into plasmid and chromosomal target sites in Drosophila melanogster embryos, indicating that DNA replication can mitigate effects of chromatinization.Our results provide an experimental foundation for the development of group II intron-based gene targeting methods for higher organisms

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Recent progress in understanding and projecting regional and global mean sea-level change

Considerable progress has been made in understanding the present and future regional and global sea level in the 2 years since the publication of the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change. Here, we evaluate how the new results affect the AR5’s assessment of (i) historical sea level rise, including attribution of that rise and implications for the sea level budget, (ii) projections of the components and of total global mean sea level (GMSL), and (iii) projections of regional variability and emergence of the anthropogenic signal. In each of these cases, new work largely provides additional evidence in support of the AR5 assessment, providing greater confidence in those findings. Recent analyses confirm the twentieth century sea level rise, with some analyses showing a slightly smaller rate before 1990 and some a slightly larger value than reported in the AR5. There is now more evidence of an acceleration in the rate of rise. Ongoing ocean heat uptake and associated thermal expansion have continued since 2000, and are consistent with ocean thermal expansion reported in the AR5. A significant amount of heat is being stored deeper in the water column, with a larger rate of heat uptake since 2000 compared to the previous decades and with the largest storage in the Southern Ocean. The first formal detection studies for ocean thermal expansion and glacier mass loss since the AR5 have confirmed the AR5 finding of a significant anthropogenic contribution to sea level rise over the last 50 years. New projections of glacier loss from two regions suggest smaller contributions to GMSL rise from these regions than in studies assessed by the AR5; additional regional studies are required to further assess whether there are broader implications of these results. Mass loss from the Greenland Ice Sheet, primarily as a result of increased surface melting, and from the Antarctic Ice Sheet, primarily as a result of increased ice discharge, has accelerated. The largest estimates of acceleration in mass loss from the two ice sheets for 2003–2013 equal or exceed the acceleration of GMSL rise calculated from the satellite altimeter sea level record over the longer period of 1993–2014. However, when increased mass gain in land water storage and parts of East Antarctica, and decreased mass loss from glaciers in Alaska and some other regions are taken into account, the net acceleration in the ocean mass gain is consistent with the satellite altimeter record. New studies suggest that a marine ice sheet instability (MISI) may have been initiated in parts of the West Antarctic Ice Sheet (WAIS), but that it will affect only a limited number of ice streams in the twenty-first century. New projections of mass loss from the Greenland and Antarctic Ice Sheets by 2100, including a contribution from parts of WAIS undergoing unstable retreat, suggest a contribution that falls largely within the likely range (i.e., two thirds probability) of the AR5. These new results increase confidence in the AR5 likely range, indicating that there is a greater probability that sea level rise by 2100 will lie in this range with a corresponding decrease in the likelihood of an additional contribution of several tens of centimeters above the likely range. In view of the comparatively limited state of knowledge and understanding of rapid ice sheet dynamics, we continue to think that it is not yet possible to make reliable quantitative estimates of future GMSL rise outside the likely range. Projections of twenty-first century GMSL rise published since the AR5 depend on results from expert elicitation, but we have low confidence in conclusions based on these approaches. New work on regional projections and emergence of the anthropogenic signal suggests that the two commonly predicted features of future regional sea level change (the increasing tilt across the Antarctic Circumpolar Current and the dipole in the North Atlantic) are related to regional changes in wind stress and surface heat flux. Moreover, it is expected that sea level change in response to anthropogenic forcing, particularly in regions of relatively low unforced variability such as the low-latitude Atlantic, will be detectable over most of the ocean by 2040. The east-west contrast of sea level trends in the Pacific observed since the early 1990s cannot be satisfactorily accounted for by climate models, nor yet definitively attributed either to unforced variability or forced climate change