Generalized Newton's Method based on Graphical Derivatives

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness assumption, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with well-recognized semismooth and $B$-differentiable versions of Newton's method for nonsmooth Lipschitzian equations

Adjustment of the basin-scale circulation at 26 degrees N to variations in Gulf Stream, deep western boundary current and Ekman transports as observed by the Rapid array

The Rapid instrument array across the Atlantic Ocean along 26 degrees N provides unprecedented monitoring of the basin-scale circulation. A unique feature of the Rapid array is the combination of full-depth moorings with instruments measuring temperature, salinity, pressure time series at many depths with co-located bottom pressure measurements so that dynamic pressure can be measured from surface to bottom. Bottom pressure measurements show a zonally uniform rise (and fall) of bottom pressure of 0.015 dbar on a 5 to 10 day time scale, suggesting that the Atlantic basin is filling and draining on a short time scale. After removing the zonally uniform bottom pressure fluctuations, bottom pressure variations at 4000 m depth against the western boundary compensate instantaneously for baroclinic fluctuations in the strength and structure of the deep western boundary current so there is no basin-scale mass imbalance resulting from variations in the deep western boundary current. After removing the mass compensating bottom pressure, residual bottom pressure fluctuations at the western boundary just east of the Bahamas balance variations in Gulf Stream transport. Again the compensation appears to be especially confined close to the western boundary. Thus, fluctuations in either Gulf Stream or deep western boundary current transports are compensated in a depth independent (barotropic) manner very close to the continental slope off the Bahamas. In contrast, compensation for variations in wind-driven surface Ekman transport appears to involve fluctuations in both western basin and eastern basin bottom pressures, though the bottom pressure difference fluctuations appear to be a factor of 3 too large, perhaps due to an inability to resolve small bottom pressure fluctuations after removal of larger zonal average, baroclinic, and Gulf Stream pressure components. For 4 tall moorings where time series dynamic height (geostrophic pressure) profiles can be estimated from sea surface to ocean bottom and bottom pressure can be added, there is no general correlation between surface dynamic height and bottom pressure. Dynamic height on each mooring is strongly correlated with sea surface height from satellite observations and the variability in both dynamic height and satellite sea surface height decrease sharply as the western boundary is approached

Interaction of carbon clusters with Ni(100) : Application to the nucleation of carbon nanotubes

In order to understand the first stages of the nucleation of carbon nanotubes in catalytic processes, we present a tight-binding Monte Carlo study of the stability and cohesive mechanisms of different carbon structures deposited on nickel (100) surfaces. Depending on the geometry, we obtain contrasted results. On the one hand, the analysis of the local energy distributions of flat carbon sheets, demonstrate that dangling bonds remain unsaturated in spite of the presence of the metallic catalyst. Their adhesion results from the energy gain of the surface Ni atoms located below the carbon nanostructure. On the other hand, carbon caps are stabilized by the presence of carbon atoms occupying the hollow sites of the fcc nickel structure suggesting the saturation of the dangling bonds

A prototype system for observing the Atlantic Meridional Overturning Circulation - scientific basis, measurement and risk mitigation strategies, and first results

The Atlantic Meridional Overturning Circulation (MOC) carries up to one quarter of the global northward heat transport in the Subtropical North Atlantic. A system monitoring the strength of the MOC volume transport has been operating since April 2004. The core of this system is an array of moored sensors measuring density, bottom pressure and ocean currents. A strategy to mitigate risks of possible partial failures of the array is presented, relying on backup and complementary measurements. The MOC is decomposed into five components, making use of the continuous moored observations, and of cable measurements across the Straits of Florida, and wind stress data. The components compensate for each other, indicating that the system is working reliably. The year-long average strength of the MOC is 18.7±5.6 Sv, with wind-driven and density-inferred transports contributing equally to the variability. Numerical simulations suggest that the surprisingly fast density changes at the western boundary are partially linked to westward propagating planetary wave

Simulations of a Line W-based observing system for the Atlantic meridional overturning circulation

In a series of observing system simulations, we test whether the Atlantic meridional overturning circulation (AMOC) can be observed based on the existing Line W deep western boundary array. We simulate a Line W array, which is extended to the surface and to the east to cover the basin to the Bermuda Rise. In the analyzed ocean circulation model ORCA025, such an extended Line W array captures the main characteristics of the western boundary current. Potential trans-basin observing systems for the AMOC are tested by combining the extended Line W array with a mid-ocean transport estimate obtained from thermal wind "measurements" and Ekman transport to the total AMOC (similarly to Hirschi et al., Geophys Res Lett 30(7):1413, 2003). First, we close Line W zonally supplementing the western boundary array with several "moorings" in the basin (Line W-32A degrees N). Second, we supplement the western boundary array with a combination of observations at Bermuda and the eastern part of the RAPID array at 26A degrees N (Line W-B-RAPID). Both, a small number of density profiles across the basin and also only sampling the eastern and western boundary, capture the variability of the AMOC at Line W-32A degrees N and Line W-B-RAPID. In the analyzed model, the AMOC variability at both Line W-32A degrees N and Line W-B-RAPID is dominated by the western boundary current variability. Away from the western boundary, the mid-ocean transport (east of Bermuda) shows no significant relation between the two Line W-based sections and 26A degrees N. Hence, a Line W-based AMOC estimate could yield an estimate of the meridional transport that is independent of the 26A degrees N RAPID estimate. The model-based observing system simulations presented here provide support for the use of Line W as a cornerstone for a trans-basin AMOC observing system

Features in the vertical structure of the meridional flow field over the continental rise east of Abaco, the Bahamas

Since Spring 2004, the RAPID-MOC mooring array (Monitoring the Atlantic Meridional Overturning Circulation at 26.5N) and the MOCHA array (Meridional Overturning Circulation and Heat-flux Array), have been a system continuously monitoring the Atlantic Meridional Circulation (MOC) in the subtropical North Atlantic. Using two year long current meter records (2004-2006), along with historical data (1986 – 1997), as decribed by Lee et.al. (1990) and Lee et.al. (1996) of the western boundary moorings, we analyze the vertical structure of the complex flow field in the Antilles Current (AC)/ Deep Western Boundary Current (DWBC) regim

Upper ocean manifestations of a reducing meridional overturning circulation

Most climate models predict a slowing down of the Atlantic Meridional Overturning Circulation during the 21st century. Using a 100year climate change integration of a high resolution coupled climate model, we show that a 5.3Sv reduction in the deep southward transport in the subtropical North Atlantic is balanced solely by a weakening of the northward surface western boundary current, and not by an increase in the southward transport integrated across the interior ocean away from the western boundary. This is consistent with Sverdrup balance holding to a good approximation outside of the western boundary region on decadal time scales, and may help to spatially constrain past and future change in the overturning circulation. The subtropical gyre weakens by 3.4Sv over the same period due to a weakened wind stress curl. These changes combine to give a net 8.7Sv reduction in upper western boundary transport. © 2012. American Geophysical Union. All Rights Reserved