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

Submesoscale CO2 variability across an upwelling front off Peru

As a major source for atmospheric CO2, the Peruvian upwelling region exhibits strong variability in surface fCO2 on short spatial and temporal scales. Understanding the physical processes driving the strong variability is of fundamental importance for constraining the effect of marine emissions from upwelling regions on the global CO2 budget. In this study, a frontal decay on length scales of (10 km) was observed off the Peruvian coast following a pronounced decrease in down-frontal (equatorward) wind speed with a time lag of 9 h. Simultaneously, the sea-to-air flux of CO2 on the inshore (cold) side of the front dropped from up to 80 to 10 mmol m−2 day−1, while the offshore (warm) side of the front was constantly outgassing at a rate of 10–20 mmol m−2 day−1. Based on repeated ship transects the decay of the front was observed to occur in two phases. The first phase was characterized by a development of coherent surface temperature anomalies which gained in amplitude over 6–9 h. The second phase was characterized by a disappearance of the surface temperature front within 6 h. Submesoscale mixed-layer instabilities were present but seem too slow to completely remove the temperature gradient in this short time period. Dynamics such as a pressure-driven gravity current appear to be a likely mechanism behind the evolution of the front

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

Higher sea surface temperature in the Indian Ocean during the Last Interglacial weakened the South Asian monsoon

Addressing and anticipating future South Asian monsoon changes under continuing global warming is of critical importance for the food security and socioeconomic well-being of one-quarter of the world’s population. However, climate model projections show discrepancies in future monsoon variability in South Asian monsoon domains, largely due to our still limited understanding of the monsoon response to warm climate change scenarios. Particularly, climate models are largely based on the assumption that higher solar insolation causes higher rainfall during similar warm climatic regimes, but this has not been verified by proxy data for different interglacial periods. Here, we compare Indian summer monsoon (ISM) variability during the Last Interglacial and Holocene using a sedimentary leaf wax δD and δ13C record from the northern Bay of Bengal, representing the Ganges–Brahmaputra–Meghna (G-B-M) river catchment. In combination with a seawater salinity record, our results show that ISM intensity broadly follows summer insolation on orbital scales, but ISM intensity during the Last Interglacial was lower than during the Holocene despite higher summer insolation and greenhouse gas concentrations. We argue that sustained warmer sea surface temperature in the equatorial and tropical Indian Ocean during the Last Interglacial increased convective rainfall above the ocean but dampened ISM intensity on land. Our study demonstrates that besides solar insolation, internal climatic feedbacks also play an important role for South Asian monsoon variability during warm climate states. This work can help to improve future climate model projections and highlights the importance of understanding controls of monsoonal rainfall under interglacial boundary conditions.Geological Setting and Proxy Records Results - Variations of n-Alkane δD and δ13C Values. - δDivc Values in Sediment Core 17286-1 Reflect ISM Intensity and Rainfall Amount. - ISM Rainfall Shifts in South Asia. - Vegetation Changes in South Asia. Discussion - Climatic Controls on ISM Intensity at Millennial to Orbital Time Scales. - Internal Climatic Feedback of South Asian Monsoon Variability during the Last Interglacial and the Holocene - Mechanisms Controlling Vegetation Variability in South Asia. - Perspectives. Method

Effect of Bioactive and Antimicrobial Nanoparticles on Properties and Applicability of Dental Adhesives

The aim of the study was to examine the applicability of bioactive and antibacterial nanoparticles to an experimental adhesive. The adhesive (60 wt% BisGMA, 15 wt% TEGDMA, 25 wt% HEMA) was mixed with combinations of 5 wt% methacryl-functionalized polyhedral oligomeric silsesquioxane (MA-POSS) and one kind of bioactive/antibacterial nanoparticles: 1 wt% core-shell silica-silver nanoparticle (SiO2@Ag), 1 wt% bioactive glass with bismuth (BAG-Bi) or 1 wt% calcium phosphate (CAP). Pure adhesive served as control. The physicochemical (degree of conversion (DC), linear shrinkage (LS), shear and complex viscosity, water sorption (WS), sol fraction (SF)), biological (antimicrobial effect) and bioactive (mineral precipitation) properties were investigated. DC and LS remained unchanged. The combination of BAG-Bi/MA-POSS resulted in a significantly increased WS and SF compared to control. In addition, the combination of CAP/MA-POSS slightly increased the shear viscosity of the adhesive. The addition of the nanoparticles did not influence the antimicrobial effects compared to the pure adhesive. Improved mineral inducing capacity could be detected in all nanoparticle combinations. The combination of bioactive and/or antibacterial nanoparticles showed improved mineral inducing capacity, but no antibacterial properties. The material properties were not or only slightly affected. Keywords: POSS; SiO2@Ag; antimicrobial nanoparticles; bioactive glass; bioactive nanoparticles; calcium phosphate; dental adhesive