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

Eddy Impacts on the Florida Current

The Gulf Stream in the Atlantic carries warm water northwards and forms both the return closure of the subtropical gyre as well as the upper limb of the meridional overturning circulation. Recent time series recorded east of the Bahamas at 26°N indicate that from May 2009 to April 2011, in contrast with past observations, the northward flowing Antilles Current covaried with the Gulf Stream in the Florida Straits—the Florida Current—even though the Florida and Antilles Currents are separated by banks and islands spanning 150?km. The peak-to-trough amplitude of transport variations during this period was 15?×?106?m3?s?1 for the Florida Current and 12?×?106?m3?s?1 for the Antilles Current, at time scales of 50?days to a year. From satellite observations, we show that the fluctuations in both the Florida and Antilles Currents between May 2009 and April 2011 are driven by eddy activity east of the Bahamas. Since the Florida Current time series is a critical time series for the state of the oceans, and often compared to climate models, this newly identified source of variability needs careful consideration when attributing the variability of the Florida Current to changes in the larger-scale circulations (e.g., gyre and overturning) or wind forcing.<br/

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

Determining North Atlantic meridional transport variability from pressure on the western boundary: a model investigation.

In this paper we investigate the possibility of determining North Atlantic meridional transport variability using pressure on the western boundary, focusing on the 42degN latitude of the Halifax WAVE array. We start by reviewing the theoretical foundations of this approach. Next we present results from a model analysis, both statistical and dynamic, that demonstrate the feasibility of the approach. We consider how well we can quantify the meridional transport variability at 42degN given complete knowledge of bottom pressure across the basin, and to what degree this quantification is degraded by first ignoring the effect of intervening topography, and then by using only bottom pressure on the western boundary. We find that for periods of greater than one year we can recover more than 90% of the variability of the main overturning cell at 42degN using only the western boundary pressure, provided we remove the depth-average boundary pressure signal. This signal arises from a basin mode of bottom pressure variability, which has power at all timescales, but that does not in truth have a meridional transport signal associated with it, and from the geostrophic depth-independent compensation of the Ekman transport. An additional benefit of the removal of the depth-average pressure is that this high-frequency Ekman signal, which is essentially noise as far as monitoring the MOC for climatically important changes is concerned, is clearly separated from other modes

The present and future system for measuring the Atlantic meridional overturning circulation and heat transport

of the global combined atmosphere-ocean heat flux and so is important for the mean climate of the Atlantic sector of the Northern Hemisphere. This meridional heat flux is accomplished by both the Atlantic Meridional Overturning Circulation (AMOC) and by basin-wide horizontal gyre circulations. In the North Atlantic subtropical latitudes the AMOC dominates the meridional heat flux, while in subpolar latitudes and in the subtropical South Atlantic the gyre circulations are also important. Climate models suggest the AMOC will slow over the coming decades as the earth warms, causing widespread cooling in the Northern hemisphere and additional sea-level rise. Monitoring systems for selected components of the AMOC have been in place in some areas for decades, nevertheless the present observational network provides only a partial view of the AMOC, and does not unambiguously resolve the full variability of the circulation. Additional observations, building on existing measurements, are required to more completely quantify the Atlantic meridional heat transport. A basin-wide monitoring array along 26.5°N has been continuously measuring the strength and vertical structure of the AMOC and meridional heat transport since March 31, 2004. The array has demonstrated its ability to observe the AMOC variability at that latitude and also a variety of surprising variability that will require substantially longer time series to understand fully. Here we propose monitoring the Atlantic meridional heat transport throughout the Atlantic at selected critical latitudes that have already been identified as regions of interest for the study of deep water formation and the strength of the subpolar gyre, transport variability of the Deep Western Boundary Current (DWBC) as well as the upper limb of the AMOC, and inter-ocean and intrabasin exchanges with the ultimate goal of determining regional and global controls for the AMOC in the North and South Atlantic Oceans. These new arrays will continuously measure the full depth, basin-wide or choke-point circulation and heat transport at a number of latitudes, to establish the dynamics and variability at each latitude and then their meridional connectivity. Modeling studies indicate that adaptations of the 26.5°N type of array may provide successful AMOC monitoring at other latitudes. However, further analysis and the development of new technologies will be needed to optimize cost effective systems for providing long term monitoring and data recovery at climate time scales. These arrays will provide benchmark observations of the AMOC that are fundamental for assimilation, initialization, and the verification of coupled hindcast/forecast climate models

Hybrid Newton-type method for a class of semismooth equations

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem

Constrained dogleg methods for nonlinear systems with simple bounds

We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affine-scaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is named Constrained Dogleg method. It generates only strictly feasible iterates. Global and locally fast convergence is ensured under standard assumptions. The method has been implemented in the Matlab solver CoDoSol that supports several diagonal scalings in both spherical and elliptical trust region frameworks. We give a brief account of CoDoSol and report on the computational experience performed on a number of representative test problem