The effect of finite rank perturbations on Jordan chains of linear operators

A general result on the structure and dimension of the root subspaces of a matrix or a linear operator under finite rank perturbations is proved: The increase of dimension from the $n$-th power of the kernel of the perturbed operator to the $(n+1)$-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation and this bound is sharp

Key lessons learned on international engagement

This briefing paper summarises shifts in international engagement in South Sudan from humanitarian aid to development and institution-building, and then back again to crisis response. The findings emerge from the recent report, Trajectories of international engagement with state and local actors: Evidence from South Sudan [^] , as well as other SLRC South Sudan research over the life of the programme. In the wake of South Sudan’s Comprehensive Peace Agreement in 2005, optimism abounded that investment in state-building would produce numerous benefits including peace, stability, growth and economic opportunities. But such optimism proved to be unfounded. This paper analyses why current aid frameworks have been mostly unsuccessful in their efforts to promote sustainable institutions and peace in South Sudan. The central argument is that aid actors largely failed because they applied technical solutions to political problems. What is needed is a rethink in approaches, modalities, and time frames, and better use of contextual and political analysis, in order to avoid similar failures in the future

Livelihoods and conflict in South Sudan

More than five million people in South Sudan are currently in urgent need of humanitarian aid, with nearly one-and-a-half million displaced and another one million refugees. These figures indicate large-scale loss of lives and extreme disruption to livelihoods, which will take decades or generations to recover from. Yet livelihoods are often just expected to recover in a post-conflict environment. Findings from six years of research by SLRC do not support this argument; in some areas of South Sudan, support for livelihoods may have even been better during conflict. This briefing paper recommends a rethink in the way that aid actors approach questions of recovery and livelihood. Rather than a simplistic either/ or approach, what is needed is a much more localised and deeper analysis of conflict, inter-communal grievances and inter-communal relations

Hydrography of the Gulf of Mexico using autonomous floats

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 773-794, doi:10.1175/JPO-D-17-0205.1.Fourteen autonomous profiling floats, equipped with CTDs, were deployed in the deep eastern and western basins of the Gulf of Mexico over a four-year interval (July 2011–August 2015), producing a total of 706 casts. This is the first time since the early 1970s that there has been a comprehensive survey of water masses in the deep basins of the Gulf, with better vertical resolution than available from older ship-based surveys. Seven floats had 14-day cycles with parking depths of 1500 m, and the other half from the U.S. Argo program had varying cycle times. Maps of characteristic water masses, including Subtropical Underwater, Antarctic Intermediate Water (AAIW), and North Atlantic Deep Water, showed gradients from east to west, consistent with their sources being within the Loop Current (LC) and the Yucatan Channel waters. Altimeter SSH was used to characterize profiles being in LC or LC eddy water or in cold eddies. The two-layer nature of the deep Gulf shows isotherms being deeper in the warm anticyclonic LC and LC eddies and shallower in the cold cyclones. Mixed layer depths have an average seasonal signal that shows maximum depths (~60 m) in January and a minimum in June–July (~20 m). Basin-mean steric heights from 0–50-m dynamic heights and altimeter SSH show a seasonal range of ~12 cm, with significant interannual variability. The translation of LC eddies across the western basin produces a region of low homogeneous potential vorticity centered over the deepest part of the western basin.The authors were supported by the Department of the Interior, Bureau of Ocean Energy Management (BOEM), Contract M08PC20043 to Leidos, Inc., Raleigh, North Carolina.2018-10-0

Deep eddies in the Gulf of Mexico observed with floats

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 2703-2719, doi:10.1175/JPO-D-17-0245.1.A new set of deep float trajectory data collected in the Gulf of Mexico from 2011 to 2015 at 1500- and 2500-m depths is analyzed to describe mesoscale processes, with particular attention paid to the western Gulf. Wavelet analysis is used to identify coherent eddies in the float trajectories, leading to a census of the basinwide coherent eddy population and statistics of the eddies’ kinematic properties. The eddy census reveals a new formation region for anticyclones off the Campeche Escarpment, located northwest of the Yucatan Peninsula. These eddies appear to form locally, with no apparent direct connection to the upper layer. Once formed, the eddies drift westward along the northern edge of the Sigsbee Abyssal Gyre, located in the southwestern Gulf of Mexico over the abyssal plain. The formation mechanism and upstream sources for the Campeche Escarpment eddies are explored: the observational data suggest that eddy formation may be linked to the collision of a Loop Current eddy with the western boundary of the Gulf. Specifically, the disintegration of a deep dipole traveling under the Loop Current eddy Kraken, caused by the interaction with the northwestern continental slope, may lead to the acceleration of the abyssal gyre and the boundary current in the Bay of Campeche region.The authors were supported by the Department of the Interior, Bureau of Ocean Energy Management (BOEM), Contract M10PC00112 to Leidos, Inc., Raleigh, North Carolina.2019-05-0

Variations in sea surface roughness induced by the 2004 Sumatra-Andaman tsunami

Observations of tsunamis away from shore are critically important for improving early warning systems and understanding of tsunami generation and propagation. Tsunamis are difficult to detect and measure in the open ocean because the wave amplitude there is much smaller than it is close to shore. Currently, tsunami observations in deep water rely on measurements of variations in the sea surface height or bottom pressure. Here we demonstrate that there exists a different observable, specifically, ocean surface roughness, which can be used to reveal tsunamis away from shore. The first detailed measurements of the tsunami effect on sea surface height and radar backscattering strength in the open ocean were obtained from satellite altimeters during passage of the 2004 Sumatra-Andaman tsunami. Through statistical analyses of satellite altimeter observations, we show that the Sumatra-Andaman tsunami effected distinct, detectable changes in sea surface roughness. The magnitude and spatial structure of the observed variations in radar backscattering strength are consistent with hydrodynamic models predicting variations in the near-surface wind across the tsunami wave front. Tsunami-induced changes in sea surface roughness can be potentially used for early tsunami detection by orbiting microwave radars and radiometers, which have broad surface coverage across the satellite ground track

Dominant circulation patterns of the deep Gulf of Mexico

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 511-529, doi:10.1175/JPO-D-17-0140.1.The large-scale circulation of the bottom layer of the Gulf of Mexico is analyzed, with special attention to the historically least studied western basin. The analysis is based on 4 years of data collected by 158 subsurface floats parked at 1500 and 2500 m and is complemented with data collected by current meter moorings in the western basin during the same period. Three main circulation patterns stand out: a cyclonic boundary current, a cyclonic gyre in the abyssal plain, and the very high eddy kinetic energy observed in the eastern Gulf. The boundary current and the cyclonic gyre appear as distinct features, which interact in the western tip of the Yucatan shelf. The persistence and continuity of the boundary current is addressed. Although high variability is observed, the boundary flow serves as a pathway for water to travel around the western basin in approximately 2 years. An interesting discovery is the separation of the boundary current over the northwestern slope of the Yucatan shelf. The separation and retroflection of the along-slope current appears to be a persistent feature and is associated with anticyclonic eddies whose genesis mechanism remains to be understood. As the boundary flow separates, it feeds into the westward flow of the deep cyclonic gyre. The location of this gyre—named the Sigsbee Abyssal Gyre—coincides with closed geostrophic contours, so eddy–topography interaction via bottom form stresses may drive this mean flow. The contribution to the cyclonic vorticity of the gyre by modons traveling under Loop Current eddies is discussed.This work was supported by the Bureau of Ocean Energy Management (BOEM) under Contract M10PC00112 assigned to Leidos, Inc

Linguistics

Contains reports on five research projects.National Institute of Mental Health (Grant 5 PO1 MH-13390-04