Hitting and returning to rare events for all alpha-mixing processes

We prove that for any a-mixing stationary process the hitting time of any n-string A(n) converges, when suitably normalized, to an exponential law. We identify the normalization constant lambda(A(n)). A similar statement holds also for the return time. To establish this result we prove two other results of independent interest. First, we show a relation between the rescaled hitting time and the rescaled return time, generalizing a theorem of Haydn, Lacroix and Vaienti. Second, we show that for positive entropy systems, the probability of observing any n-string in n consecutive observations goes to zero as n goes to infinity. (c) 2010 Elsevier B.V. All rights reserved.

Improvign mixing processes with the help of numerical tools

In several industrial applications, highly complex behaviour materials are used together with intricate mixing processes, which difficult the achievement of the desired properties for the produced materials. This is the case of the well-known dispersion of nano-sized fillers in a melt polymer matrix, used to improve the nanocomposite mechanical and/or electrical properties. This mixing is usually performed in twin-screw extruders, that promote complex flow patterns, and, since an in loco analysis of the material evolution and mixing is difficult to perform, numerical tools can be very useful to predict the evolution and behaviour of the material. This work presents a numerical based study to improve the understanding of mixing processes. Initial numerical studies were performed with generalized Newtonian fluids, but, due to the null relaxation time that characterize this type of fluids, the assumption of viscoelastic behavior was required. Therefore, the polymer melt was rheologically characterized, and, a six mode Phan-Thien-Tanner and Giesekus models were used to fit the rheological data. These viscoelastic rheological models were used to model the process. The conclusions obtained in this work provide additional and useful data to correlate the type and intensity of the deformation history promoted to the polymer nanocomposite and the quality of the mixing obtained.

Carbon and oxygen isotope study of hydrothermal carbonates in the zinc-lead deposits of the San Vicente district, central Peru: A quantitative modeling on mixing processes and CO2 degassing

Carbon and oxygen isotope studies of the host and gangue carbonates of Mississippi Valley-type zinc-lead deposits in the San Vicente District hosted in the Upper Triassic to Lower Jurassic dolostones of the Pucara basin (central Peru) were used to constrain models of the ore formation. A mixing model between an incoming hot saline slightly acidic radiogenic (Pb, Sr) fluid and the native formation water explains the overall isotopic variation (delta(13)C = - 11.5 to + 2.5 parts per thousand relative to PDB and delta(18)O = + 18.0 to + 24.3 parts per thousand relative to SMOW) of the carbonate generations. The dolomites formed during the main ore stage show a narrower range (delta(13)C = - 0.1 to + 1.7 parts per thousand and delta(18)O = + 18.7 to + 23.4 parts per thousand) which is explained by exchange between the mineralizing fluids and the host carbonates combined with changes in temperature and pressure. This model of fluid-rock interaction explains the pervasive alteration of the host dolomite I and precipitation of sphalerite I. The open-space filling hydrothermal white sparry dolomite and the coexisting sphalerite II formed by prolonged fluid-host dolomite interaction and limited CO2 degassing. Late void-filling dolomite III (or calcite) and the associated sphalerite III formed as the consequence of CO2 degassing and concomitant pH increase of a slightly acidic ore fluid. Widespread brecciation is associated to CO2 outgassing. Consequently, pressure variability plays a major role in the ore precipitation during the late hydrothermal events in San Vicente. The presence of native sulfur associated with extremely carbon-light calcites replacing evaporitic sulfates (e.g., delta(13)C = - 11.5 parts per thousand), altered native organic matter and heavier hydrothermal bitumen (from - 27.0 to - 23.0 parts per thousand delta(13)C) points to thermochemical reduction of sulfate and/or thiosulfate. The delta(13)C- and delta(18)O-values of the altered host dolostone and hydrothermal carbonates, and the carbon isotope composition of the associated organic matter show a strong regional homogeneity. These results coupled with the strong mineralogical and petrographic similarities of the different MVT occurrences perhaps reflects the fact that the mineralizing processes were similar in the whole San Vicente belt, suggesting the existence of a common regional mineralizing hydrothermal system with interconnected plumbing.

An evaluation of the inorganic and organic geochemistry of the San Vicente Mississippi Valley-type zinc-lead district, central Peru: Implications for ore fluid composition, mixing processes, and sulfate reduction

Mississippi Tialley-type zinc-lead deposits and ore occurrences in the San Vicente belt are hosted in dolostones of the eastern Upper Triassic to Lower Jurassic Pucara basin, central Peru. Combined inorganic and organic geochemical data from 22 sites, including the main San Vicente deposit, minor ore occurrences, and barren localities, provide better understanding of fluid pathways and composition, ore precipitation mechanisms, Eh-pH changes during mineralization, and relationships between organic matter and ore formation. Ore-stage dark replacement dolomite and white sparry dolomite are Fe and rare earth element (REE) depleted, and Mn enriched, compared to the host dolomite. In the main deposit, they display significant negative Ce and probably Eu anomalies. Mixing of an incoming hot, slightly oxidizing, acidic brine (H2CO3 being the dominant dissolved carbon species), probably poor in REE and Fe, with local intraformational, alkaline, reducing waters explains the overall carbon and oxygen isotope variation and the distributions of REE and other trace elements in the different hydrothermal carbonate generations. The incoming ore fluid flowed through major aquifers, probably basal basin detrital units, with limited interaction with the carbonate host rocks. The hydrothermal carbonates show a strong regional chemical homogeneity, indicating access of the ore fluids by interconnected channelways near the ore occurrences. Negative Ce anomalies in the main deposit, that are absent at the district scale, indicate local ore-fluid chemical differences. Oxidation of both migrated and indigenous hydrocarbons by the incoming fluid provided the local reducing conditions necessary for sulfate reduction to H2S, pyrobitumen precipitation, and reduction of Eu3+ to Eu2+. Fe-Mn covariations, combined with the REE contents of the hydrothermal carbonates, are consistent with the mineralizing system shifting from reducing/rock-dominated to oxidizing/fluid-dominated conditions following ore deposition. Sulfate and sulfide sulfur isotopes support sulfide origin from evaporite-derived sulfate by thermochemical organic reduction; further evidence includes the presence of C-13-depleted calcite cements (similar to-12 parts per thousand delta(13)C) as sulfate pseudomorphs, elemental sulfur, altered organic matter in the host dolomite, and isotopically heavier, late, solid bitumen. Significant alteration of the indigenous and extrinsic hydrocarbons, with absent bacterial membrane biomarkers (hopanes) is observed. The light delta(34)S of sulfides from small mines and occurrences compared to the main deposit reflect a local contribution of isotopically light sulfur, evidence of local differences in the ore-fluid chemistry.

Investigating stellar mixing processes through the study of the Red-Giant Branch bump

Extra mixing at the borders of convective zones in stellar interiors takes on an important role in the chemical evolution of stars and galaxies through the transport of chemical elements towards the stellar surface: knowing the overshooting mechanism can therefore lead to a better understanding of the observed chemical abundances in stellar photospheres. The comprehension of this phenomenon is quite uncertain and currently object of many studies. In particular, concerning low mass stars, in the past decades several works highlighted a discrepancy between the observed luminosity of the Red-Giant Branch bump and its prediction from simulations, which can be fixed including overshooting at the base of the convective envelope. This work, studying the Red-Giant Branch bump and using it as a diagnostic for extra mixing processes, tries to classify two different types of overshooting, instantaneous and diffusive, using both simulations from stellar models and Globular Clusters’ data. The aim is to understand which one of the two mixing processes is the most suitable in reproducing the observed stellar behaviour and, in case both of them provide reliable results, what are the conditions under which they produce the same effects on the Red-Giant Branch bump luminosity function and are consequently indistinguishable. Finally, possible dependences of overshooting efficiency on stellar parameters, such as chemical composition, are analysed.

Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing

Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of 5 x 10(9) atoms/cm(3). Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to seed the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.

Mixing of Rhône River water in Lake Geneva (Switzerland-France) inferred from stable hydrogen and oxygen isotope profiles

Depth profiles were sampled at different locations throughout Lake Geneva on a monthly and seasonal basis over the course of 2 years and analysed for their stable hydrogen and oxygen isotope compositions. The isotopic compositions indicate an isotopic stratification in the metalimnion during summer and fall. This is related to mixing of Rhône River water, which in summer is dominated by snow and glacier melt waters, and lake water, with the latter having a homogenous isotopic composition. The observed interflow layer is 7-15 m thick and can be traced by the distinct stable isotope composition of the water for about 55 km throughout the lake as well as into shallow bay regions. Depth of the interflow layer close to the Rhône River mouth is similar to those previously described based on echo-soundings and turbidity profiles of sediment dispersion. In contrast to previous descriptions of the interflow within Lake Geneva, the stable isotope compositions allow for direct, natural tracing of the Rhône River water even in cases where the turbidity and conductivity measurements do not indicate such an interflow. In addition, the method allows for a quantification of the Rhône River and lake water in the interflow with the fraction of Rhône River water within the interflow estimated to be up to 37% in summer. The isotopic composition further indicates different vertical mixing processes within the two lake basins of Lake Geneva, related to the density gradients and local stability within the water column. The method may be applicable to other lakes in catchments with large differences in the topography as water that originates from high altitudes or glaciers has a distinct oxygen and hydrogen isotope composition compared to other sources of water originating at lower altitudes and/or from direct precipitation over the lake. Stable isotope measurements thus improve the understanding of the circulation of water within the lake, which is fundamental for an evaluation of the water residence times, dissolved pollutant and nutrient transport as well as oxygenation.

Tracing of the Rhône River, wastewater, and mixing within Lake Geneva : stable isotope compositions of water and dissolved inorganic carbon

This study presents an evaluation of the stable isotopic composition of water (hydrogen and oxygen) and dissolved inorganic carbon (DIC) of Lake Geneva, a deep, peri-alpine lake situated at the border between Switzerland and France. The research goal is to apply vertical and seasonal variations of the isotope compositions to evaluate mixing processes of pollutants, nutrients and oxygen. Depth profiles were sampled at different locations throughout Lake Geneva on a monthly and seasonal basis over the course of three years (2009-2011). The results of the oxygen isotopic composition indicate a Rhône River interflow, which can be traced for about 55 km throughout the lake during summer. The Rhône River interflow is 7 to 15 m thick and the molar fraction of Rhône water is estimated to amount up to 37 %. Calculated density of the water and measured isotopic compositions demonstrate that the interflow depth changes in conjunction with the density gradient in the water column during fall. Partial pressure of CO2 indicates that the epilimnion is taking up CO2 from the atmosphere between spring and fall. The epilimnion is most enriched in 13CDIC in September and a progressive depletion of 13CDIC can be observed in the metalimnion from spring to late fall. This stratification is dependent on the local density stratification and the results demonstrate that parameters, which are indicating photosynthesis, are not necessarily linked to δ13CDIC values. In addition, the amount of primary production shows a strong discrepancy between summer 2009 and 2010, but δ13CDIC values of the epilimnion and metalimnion do not indicate variations. In the hypolimnion of the deep lake δ13CDIC values are constant and the progressive depletion allows tracing remineralization processes. The combination of stable carbon and oxygen isotopic compositions allows furthermore tracing Rhône River water fractions, as well as wastewater, stormwater and anthropogenic induced carbon in the water column of the shallow Bay of Vidy. In combination with the results of measured micropollutants, the study underlines that concentrations of certain substances may be related to the Rhône River interflow and/or remineralization of particulate organic carbon. Water quality monitoring and research should therefore be extended to the metalimnion as well as sediment water interface.

Ocean heat uptake processes: a model intercomparison

We compare the quasi-equilibrium heat balances, as well as their responses to 4×CO2 perturbation, among three global climate models with the aim to identify and explain inter-model differences in ocean heat uptake (OHU) processes. We find that, in quasi-equilibrium, convective and mixed layer processes, as well as eddy-related processes, cause cooling of the subsurface ocean. The cooling is balanced by warming caused by advective and diapycnally diffusive processes. We also find that in the CO2-perturbed climates the largest contribution to OHU comes from changes in vertical mixing processes and the mean circulation, particularly in the extra-tropics, caused both by changes in wind forcing, and by changes in high-latitude buoyancy forcing. There is a substantial warming in the tropics, a significant part of which occurs because of changes in horizontal advection in extra-tropics. Diapycnal diffusion makes only a weak contribution to the OHU, mainly in the tropics, due to increased stratification. There are important qualitative differences in the contribution of eddy-induced advection and isopycnal diffusion to the OHU among the models. The former is related to the different values of the coefficients used in the corresponding scheme. The latter is related to the different tapering formulations of the isopycnal diffusion scheme. These differences affect the OHU in the deep ocean, which is substantial in two of the models, the dominant region of deep warming being the Southern Ocean. However, most of the OHU takes place above 2000 m, and the three models are quantitatively similar in their global OHU efficiency and its breakdown among processes and as a function of latitude.

Southern Ocean isopycnal mixing and ventilation changes driven by winds

Observed and predicted changes in the strength of the westerly winds blowing over the Southern Ocean have motivated a number of studies of the response of the Antarctic Circumpolar Current and Southern Ocean Meridional Overturning Circulation (MOC) to wind perturbations and led to the discovery of the``eddy-compensation" regime, wherein the MOC becomes insensitive to wind changes. In addition to the MOC, tracer transport also depends on mixing processes. Here we show, in a high-resolution process model, that isopycnal mixing by mesoscale eddies is strongly dependent on the wind strength. This dependence can be explained by mixing-length theory and is driven by increases in eddy kinetic energy; the mixing length does not change strongly in our simulation. Simulation of a passive ventilation tracer (analogous to CFCs or anthropogenic CO$_2$) demonstrates that variations in tracer uptake across experiments are dominated by changes in isopycnal mixing, rather than changes in the MOC. We argue that, to properly understand tracer uptake under different wind-forcing scenarios, the sensitivity of isopycnal mixing to winds must be accounted for.

Mixing properties of ester-containing solutions: a study on the ternary (methyl alkanoate (pentanoate and methanoate)+methanol and the corresponding binaries. New contributions to the (ester+ester) interactions

[EN]This work studies the volumetric (VE m) and energetic (HE m) properties resulting from the mixing processes of binary systems and the corresponding ternary of two methyl esters (methanoate and pentanoate) with methanol. The three binaries produce net endothermic mixing effects, with important energetic interactions, with maximum values of HE m ffi 400 J mol 1 , for the (ester + ester) system. This produces expansive effects VE m > 0, but the binaries of the (methyl esters + methanol) give rise to contractions VE m < 0, due to the formation of molecular aggregates.

Tidal-induced mixing and diapycnal nutrient fluxes in the Mauritanian upwelling region

The Mauritanian coastal area is one of the most biologically productive upwelling regions in the world ocean. Shipboard observations carried out during maximum upwelling season and short-term moored observations are used to investigate diapycnal mixing processes and to quantify diapycnal fluxes of nutrients. The observations indicate strong tide-topography interactions that are favored by near-critical angles occurring on large parts of the continental slope. Moored velocity observations reveal the existence of highly nonlinear internal waves and bores and levels of internal wave spectra are strongly elevated near the buoyancy frequency. Dissipation rates of turbulent kinetic energy at the slope and shelf determined from microstructure measurements in the upper 200 m averages to ? = 5 × 10-8 W kg-1. Particularly elevated dissipation rates were found at the continental slope close to the shelf break, being enhanced by a factor of 100 to 1000 compared to dissipation rates farther offshore. Vertically integrated dissipation rates per unit volume are strongest at the upper continental slope reaching values of up to 30 mW m-2. A comparison of fine-scale parameterizations of turbulent dissipation rates for shelf regions and the open ocean to the measured dissipation rates indicates deficiencies in reproducing the observations. Diapycnal nitrate fluxes above the continental slope at the base of the mixed layer yielding a mean value of 12 × 10-2 µmol m-2 s-1 are amongst the largest published to date. However, they seem to only represent a minor contribution (10% to 25%) to the net community production in the upwelling region.

On the driving processes of the Atlantic meridional overturning circulation

Because of its relevance for the global climate the Atlantic meridional overturning circulation (AMOC) has been a major research focus for many years. Yet the question of which physical mechanisms ultimately drive the AMOC, in the sense of providing its energy supply, remains a matter of controversy. Here we review both observational data and model results concerning the two main candidates: vertical mixing processes in the ocean's interior and wind-induced Ekman upwelling in the Southern Ocean. In distinction to the energy source we also discuss the role of surface heat and freshwater fluxes, which influence the volume transport of the meridional overturning circulation and shape its spatial circulation pattern without actually supplying energy to the overturning itself in steady state. We conclude that both wind-driven upwelling and vertical mixing are likely contributing to driving the observed circulation. To quantify their respective contributions, future research needs to address some open questions, which we outline.