Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Molecular Dynamics of Thermotropic Liquid Crystals: Anomalous relaxation dynamics of calamitic and discotic liquid crystals

Recent optical kerr effect (OKE) studies have demonstrated that orientational relaxation of rod-like nematogens exhibits temporal power law decay at intermediate times not only near the isotropic–nematic (I–N) phase boundary but also in the nematic phase. Such behaviour has drawn an intriguing analogy with supercooled liquids. We have investigated both collective and single-particle orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I–N phase boundary, the system behaves remarkably like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system. A model liquid crystal, consisting of disk-like molecules, has also been investigated in molecular dynamics simulations for orientational relaxation along two isobars starting from the high temperature isotropic phase. The isobars have been so chosen that the phase sequence isotropic (I)–nematic (N)–columnar (C) appears upon cooling along one of them and the sequence isotropic (I)–columnar(C) along the other. While the orientational relaxation in the isotropic phase near the I–N phase transition shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I–C phase boundary. The origin of the power law decay in the single-particle second-rank orientational time correlation function (OTCF) is traced to the growth of the orientational pair distribution functions near the I–N phase boundary. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational OTCF follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

A nearly constant switching frequency current hysteresis controller with generalized parabolic boundaries using 12-sided polygonal voltage space vectors for IM drives

In this paper, a current hysteresis controller with parabolic boundaries for a 12-sided polygonal voltage space vector inverter fed induction motor (IM) drive is proposed. Parabolic boundaries with generalized vector selection logic, valid for all sectors and rotational direction, is used in the proposed controller. The current error space phasor boundary is obtained by first studying the drive scheme with space vector based PWM (SVPWM) controller. Four parabolas are used to approximate this current error space phasor boundary. The system is then run with space phasor based hysteresis PWM controller by limiting the current error space vector (CESV) within the parabolic boundary. The proposed controller has simple controller implementation, nearly constant switching frequency, extended modulation range and fast dynamic response with smooth transition to the over modulation region.

Biomass changes and trophic amplification of plankton in a warmer ocean

Ocean warming can modify the ecophysiology and distribution of marine organisms, and relationships between species, with nonlinear interactions between ecosystem components potentially resulting in trophic amplification. Trophic amplification (or attenuation) describe the propagation of a hydroclimatic signal up the food web, causing magnification (or depression) of biomass values along one or more trophic pathways. We have employed 3-D coupled physical-biogeochemical models to explore ecosystem responses to climate change with a focus on trophic amplification. The response of phytoplankton and zooplankton to global climate-change projections, carried out with the IPSL Earth System Model by the end of the century, is analysed at global and regional basis, including European seas (NE Atlantic, Barents Sea, Baltic Sea, Black Sea, Bay of Biscay, Adriatic Sea, Aegean Sea) and the Eastern Boundary Upwelling System (Benguela). Results indicate that globally and in Atlantic Margin and North Sea, increased ocean stratification causes primary production and zooplankton biomass to decrease in response to a warming climate, whilst in the Barents, Baltic and Black Seas, primary production and zooplankton biomass increase. Projected warming characterized by an increase in sea surface temperature of 2.29 ± 0.05 °C leads to a reduction in zooplankton and phytoplankton biomasses of 11% and 6%, respectively. This suggests negative amplification of climate driven modifications of trophic level biomass through bottom-up control, leading to a reduced capacity of oceans to regulate climate through the biological carbon pump. Simulations suggest negative amplification is the dominant response across 47% of the ocean surface and prevails in the tropical oceans; whilst positive trophic amplification prevails in the Arctic and Antarctic oceans. Trophic attenuation is projected in temperate seas. Uncertainties in ocean plankton projections, associated to the use of single global and regional models, imply the need for caution when extending these considerations into higher trophic levels.

Diazotrophic activity of Trichodesmium and unicellular cyanobacteria in the subtropical NE Atlantic

Programa de Doctorado en Oceanografía

Two Stable Equilibria of the Atlantic Subpolar Gyre

The cyclonic circulation of the Atlantic subpolar gyre is a key mechanism for North Atlantic climate variability on a wide range of time scales. It is generally accepted that it is driven by both cyclonic winds and buoyancy forcing, yet the individual importance and dynamical interactions of the two contributions remain unclear. The authors propose a simplified four-box model representing the convective basin of the Labrador Sea and its shallow and deep boundary current system, the western subpolar gyre. Convective heat loss drives a baroclinic flow of relatively light water around the dense center. Eddy salt flux from the boundary current to the center increases with a stronger circulation, favors the formation of dense waters, and thereby sustains a strong baroclinic flow, approximately 10%–25% of the total. In contrast, when the baroclinic flow is not active, surface waters may be too fresh to convect, and a buoyancy-driven circulation cannot develop. This situation corresponds to a second stable circulation mode. A hysteresis is found for variations in surface freshwater flux and the salinity of the near-surface boundary current. An analytical solution is presented and analyzed.

Stable isotope record and lithic fragments distribution in sediments of MIS9-14 of the North Atlantic

Stable isotope and ice-rafted debris records from three core sites in the mid-latitude North Atlantic (IODP Site U1313, MD01-2446, MD03-2699) are combined with records of ODP Sites 1056/1058 and 980 to reconstruct hydrographic conditions during the middle Pleistocene spanning Marine Isotope Stages (MIS) 9-14 (300-540 ka). Core MD03-2699 is the first high-resolution mid-Brunhes record from the North Atlantic's eastern boundary upwelling system covering the complete MIS 11c interval and MIS 13. The array of sites reflect western and eastern basin boundary current as well as north to south transect sampling of subpolar and transitional water masses and allow the reconstruction of transport pathways in the upper limb of the North Atlantic's circulation. Hydrographic conditions in the surface and deep ocean during peak interglacial MIS 9 and 11 were similar among all the sites with relative stable conditions and confirm prolonged warmth during MIS 11c also for the mid-latitudes. Sea surface temperature (SST) reconstructions further reveal that in the mid-latitude North Atlantic MIS 11c is associated with two plateaus, the younger one of which is slightly warmer. Enhanced subsurface northward heat transport in the eastern boundary current system, especially during early MIS 11c, is denoted by the presence of tropical planktic foraminifer species and raises the question how strongly it impacted the Portuguese upwelling system. Deep water ventilation at the onset of MIS 11c significantly preceded surface water ventilation. Although MIS 13 was generally colder and more variable than the younger interglacials the surface water circulation scheme was the same. The greatest differences between the sites existed during the glacial inceptions and glacials. Then a north - south trending hydrographic front separated the nearshore and offshore waters off Portugal. While offshore waters originated from the North Atlantic Current as indicated by the similarities between the records of IODP Site U1313, ODP Site 980 and MD01-2446, nearshore waters as recorded in core MD03-2699 derived from the Azores Current and thus the subtropical gyre. Except for MIS 12, Azores Current influence seems to be related to eastern boundary system dynamics and not to changes in the Atlantic overturning circulation.

Surface sediment analyses, bivalve and gastropod taxa of marine sediments from the Banc d'Arguin, Mauritania

High-nutrient tropical carbonate systems are known to produce sediments that, in terms of skeletal composition, are reminiscent of their extra-tropical counterparts. Such carbonate systems and associated carbonate grain assemblages in the tropics are rare in the present-day world. Nonetheless, it is crucial to gain a better understanding of those ecosystems, including their drivers and players because such settings potentially represent models for ancient depositional systems as well as for predicted future environmental conditions. One of the modern occurrences of eutrophic tropical carbonate systems is the northern Mauritanian Shelf. The marine environment is characterized by an eastern boundary upwelling system that pushes cool and nutrient-rich intermediate waters onto a wide epicontinental platform (Golfe d'Arguin) where the waters warm up to tropical temperatures. The resulting facies is mixed carbonate-siliciclastic with a dominant foramol association grading into bimol and barnamol grain assemblages in the shallowest areas forming the Banc d'Arguin. Besides this cool water-related heterozoan association, the carbonate sediment is characterized by tropical molluskan species, while chlorozoan biota (e.g., corals and algal symbiont-bearing foraminifers) are entirely absent. We here present a first comprehensive facies analysis of this model example of eutrophic tropical carbonates. Furthermore, we reconstruct the loci of carbonate production and provide a conclusive depositional model of the Banc d'Arguin that received little attention to date due to its poorly accessible nature.

Sea surface temperature record of ODP Site 202-1233

We present the first high-resolution alkenone-derived sea surface temperature (SST) reconstruction in the southeast Pacific (Ocean Drilling Program Site 1233) covering the major part of the last glacial period and the Holocene. The record shows a clear millennial-scale pattern that is very similar to climate fluctuations observed in Antarctic ice cores, suggesting that the Southern Hemisphere high-latitude climate changes extended into the midlatitudes, involving simultaneous changes in air temperatures over Antarctica, sea ice extent, extension of the Antarctic Circumpolar Current, and westerly atmospheric circulation. A comparison to other midlatitude surface ocean records suggests that this "Antarctic" millennial-scale pattern was probably a hemisphere-wide phenomenon. In addition, we performed SST gradient reconstructions over the complete latitudinal range of the Pacific Eastern Boundary Current System for different time intervals during the last 70 kyr. The main results suggest an equatorward displaced subtropical gyre circulation during marine isotope stages 2 and 4.

Stable oxygen isotope record and age determination of sediments from the North Atlantic Ocean

Sea surface temperature and salinity estimates reconstructed using planktonic foraminiferal abundance and delta18O records from core SU90-03 (40°N, 32°W, 2475 m water depth) reveal large climatic fluctuations linked to major instabilities in Northern Hemisphere ice sheets over the last 150 000 years. Episodes of enhanced ice rafted detritus (IRD) input were accompanied by discrete temperature minima, representing coolings of between 4 and 8°C, and reductions in surface salinity of up to 2.5-3.5 per mil. Several additional cooling episodes of a similar magnitude were documented during intervals of low IRD input that appear to be synchronous, within the limits of dating, with ice rafting events spatially confined to higher latitudes. Accelerator mass spectrometer 14C dates for Heinrich events (H1 - 14.2 ka, H2 - 21.4 ka, H3 - 26.7 ka, H4 - 34.8 ka, H5 - 47.2 ka) obtained from core SU90-03 agree well with other published age estimates and suggest a contemporaneous pattern of climate change throughout the North Atlantic during the last glacial period. This interpretation is supported by a comparison of IRD and palaeotemperature records from DSDP site 609 and core SU90-03, which clearly shows that the major climatic fluctuations identified at high latitudes were transmitted toward the subtropics. However, 14C dates suggest that ice rafting episodes may be diachronous to some extent. The northward migration of the polar front after the H1 event at 40°N in the mid-Atlantic occurred at 14 ka, approximately 500 years earlier than along the Portuguese margin, where the southerly advection of polar waters persisted within eastern boundary current system.

Barium in sediments off northwest Africa

High-resolution down-core analyses of the solid phase content of total barium (Batot) and total organic carbon (TOC) back to 25 kyr B.P. were performed on a gravity core from the upper continental slope off Cape Yubi (Morocco). The observed discrepancy between the two potential paleoproductivity proxies, Batot and TOC, initiated supplementary examinations of the pore water, the geochemistry of the clay fraction, X-ray diffraction analyses, and the application of a sequential Ba extraction method of selected samples. Additionally, we analyzed down-core samples of the planktonic foraminifera Turborotalita quinqueloba and Globorotalia inflata for their Ba/Ca ratios. These analyses, which were performed for the first time on these species, were used to reconstruct past oceanic Ba concentrations. We suggest that in the study area, which is characterized by high accumulation rates, the preserved TOC content is a valuable proxy for past primary productivity, whereas the solid phase Batot contents appear to be affected by other mechanisms and factors. Peaks of total barium content in the clay fraction and of Ba/Ca ratios in the planktonic foraminifera shells found during the Younger Dryas and the Heinrich 1 event are likely to result from increased meltwater influx into the northern North Atlantic. We suggest that Ba-enriched meltwater was transmitted by the eastern boundary current system from higher latitudes to the region of the Canary Islands. Total barium contents of the clay fraction (Batot,clay) and Ba/Ca in planktonic foraminifera shells seem to be reliable proxies for this discharge of meltwater.

Stable isotope record of planktonic foraminifera from the western Iberian margin during marine isotope stage 2

The surface water hydrography along the western Iberian margin, as part of the North Atlantic's eastern boundary upwelling system, consists of a complex, seasonally variable system of equatorward and poleward surface and subsurface currents and seasonal upwelling. Not much information exists to ascertain if the modern current and productivity patterns subsisted under glacial climate conditions, such as during marine isotope stage (MIS) 2, and how North Atlantic meltwater events, especially Heinrich events, affected them. To help answer these questions we are combining stable isotope records of surface to subsurface dwelling planktonic foraminifer species with sea surface temperature and export productivity data for four cores distributed along the western and southwestern Iberian margin (MD95-2040, MD95-2041, MD99-2336, and MD99-2339). The records reveals that with the exception of the Heinrich events and Greenland Stadial (GS) 4 hydrographic conditions along the western Iberian margin were not much different from the present. During the Last Glacial Maximum (LGM), subtropical surface and subsurface waters penetrated poleward to at least 40.6°N (site MD95-2040). Export productivity was, in general, high on the western margin during the LGM and low in the central Gulf of Cadiz, in agreement with the modern situation. During the Heinrich events and GS 4, on the other hand, productivity was high in the Gulf of Cadiz and suppressed in the upwelling regions along the western margin where a strong halocline inhibited upwelling. Heinrich event 1 had the strongest impact on the hydrography and productivity off Iberia and was the only period when subarctic surface waters were recorded in the central Gulf of Cadiz. South of Lisbon (39°N), the impact of the other Heinrich events was diminished, and not all of them led to a significant cooling in the surface waters. Thus, climatic impacts of Heinrich events highly varied with latitude and the prevailing hydrographic conditions in this region.

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.

On a mathematical model of tumor growth based on cancer stem cells

We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show that there exists a unique homogeneous steady state which is stable.

Benthic foraminifera in Southwest Indian Ocean surface sediments

The distribution of deep-sea benthonic foraminifera in core top samples from the southwest Indian Ocean is examined. Principal component analysis reveals two major assemblages. One assemblages between 3600 and 4800-m water depth is dominated by Episominella umbonifera and is associated with cold (Theta = -0.3 to 0.8°C), low salinity (34.66 to 34.72 * 10**-3) Antarctic Bottom Water in the Crozet Basin, in fracture zones, and on the flanks of the Southwest Indian Ridge. A second assemblage, dominated by Planulina wuellerstorfi, Globocassidulina subglobasa, Astrononion echolsi and Pullenia bulloides, is between 1600 and 3800 m on the Crozet Plateau, Madagascar Ridge, Central Indian Ridge, and Southwest Indian Ridge and is associated with relatively warm (Theta = 0.8 to 2.6°C), high salinity (34.72 to 34.76 * 10**-3) North Atlantic Deep Water. The third principal component divides the P. wuellerstorfi assemblage into two subgroups. One is dominated by Epistominella exigua, P. bulloides, P. wuellerstorfi, and A. echolsi and a second is dominated by G. subglobosa. The distribution of the E. umbonifera assemblage and previous hydrographic studies suggest that AABW flows as a western boundary contour current in the Crozet Basin and penetrates fracture zones in the Southwest Indian Ridge between 55 and 57°E and near 66°E as it travels northward into the Madagascar and Mascarene basins. The faunal-water mass associations from the southeast Indian Ocean are compared; the most notable faunal difference is the absence of Uvigerina as a dominant taxon in the southwest Indian Ocean. A comparison of dissolved oxygen and Uvigerina data shows that oxygen is not a major influence upon the distribution of Uvigerina. A correlation analysis of the faunal data and water depth, potential temperature, in situ temperature, salinity, dissolved oxygen, and 1 - Omega, an index of calcium carbonate undersaturation, was carried out to determine the relationships between fauna and hydrography. The second principal component has a significant positive correlation at the 99.9% level with temperature and negative correlations with water depth and 1 - Omega. A general faunal-water mass correlation exists, but it is not possible to determine which variable controls the faunal distributions.