Metabolism of triglyceride-rich lipoproteins and lipid transfer to high-density lipoprotein in young obese and normal-weight patients with polycystic ovary syndrome

Objective: To clarify whether the metabolism of triglyceride-rich lipoproteins and lipid transfer to high-density lipoprotein (HDL) are altered in patients with polycystic ovary syndrome (PCOS). Design: Case control study. Setting: Endocrinology clinics. Patient(s): Eight normal-weight (NW) and 15 obese (013) patients with PCOS were compared with 10 NW and 10 Ob women without PCOS paired for age and body mass index. Intervention(s): Determination of triglyceride-rich lipoprotein metabolism and lipid transfer to HDL. Main Outcome Measure(s): Participants were injected triglyceride-rich emulsions labeled with (14)C-cholesteryl esters and (3)H-triglycerides and the fractional clearance rate (FCR, in min(-1)) of labels was determined. Lipid transfer from artificial nanoemulsions to HDL was performed by incubating radioactively labeled lipid nanoemulsions with plasma during 1 hour, followed by radioactive counting of HDL-containing supernatant after chemical precipitation. Result(s): Lipolysis estimated by triglyceride FCR was equal in PCOS groups (NW = 0.043 +/- 0.032, Ob = 0.033 +/- 0.009) and respective controls (NW = 0.039 +/- 0.015, Ob = 0.044 +/- 0.019). However, the remnant removal as estimated by cholesteryl ester FCR was reduced in both PCOS groups (NW = 0.005 +/- 0.006, Ob = 0.005 +/- 0.005) compared with controls (NW = 0.016 +/- 0.006, Ob = 0.011 +/- 0.072). Lipid transfer rates were not different among groups, but triglyceride transfer rates were positively correlated with homeostasis model assessment estimate of insulin resistance in PCOS. Conclusion(s): PCOS patients showed decreased removal of atherogenic remnants even when fasting glucose was <100 mg/dL. This reinforces the usefulness of the measures taken to prevent cardiovascular events in PCOS patients. (Fertil Steril (R) 2010;93:1948-56. (C)2010 by American Society for Reproductive Medicine.)

Effects of bone remodelling on calcium mass transfer during haemodialysis

Background. During haemodialysis, calcium balance can affect, or be affected by, mineral metabolism. However, when dialysate calcium concentration (d[Ca]) is chosen or kinetic models are employed to calculate calcium balance, bone remodelling is rarely considered. In this study, we examined whether bone remodelling affects calcium mass transfer during haemodialysis. Methods. We dialysed 23 patients using a d[Ca] of 1.0, 1.25, 1.5 or 1.75 mmol/L. Calcium mass transfer was measured and associated with remodelling bone factors. Results. Calcium balance varied widely depending on the d[Ca]. Calcium removal was -578 +/- 389, -468 +/- 563, +46 +/- 400 and +405 +/- 413 mg when a d[Ca] of 1.0, 1.25, 1.5 or 1.75 mmol/L was used, respectively (1.0 and 1.25 VS 1.5 and 1.75 mmol/L, P<0.001; 1.5 vs 1.75 mmol/L, P<0.05). Univariate analysis showed that calcium balance correlated with calcium gradient, parathyroid hormone (PTH), osteocalcin and dialysis vintage. Multivariate analysis revealed that calcium balance was dependent on calcium gradient, PTH and osteocalcin. Conclusions. These results suggest that bone remodelling could affect calcium mass transfer during haemodialysis.

Mass transfer correlations for rotating drum bioreactors

Evaporative cooling is extremely important for large-scale operation of rotating drum bioreactors (RDBs). Outlet water vapour concentrations were measured for a RDB containing wet wheat bran with the aim of determining the mass transfer coefficient for evaporation from the bran bed to the headspace. Mass transfer was expressed as the mass transfer coefficient times the area for transfer per unit volume of void space in the drum. Values of ka' were determined under combinations of aeration superficial velocities ranging from 0.006 to 0.017 ms(-1) and rotation rates ranging from 0 to 9 rpm. Mass transfer coefficients were evaluated using a variety of residence time distributions (RTDs) for flow in the gas phase including plug flow and well-mixed and a Central Jet RTD based on RTD studies. If plug flow is assumed, the degree of holdup at low effective Peclet (Pe(eff)) numbers gives an apparent under-estimate of ka' compared with empirical correlations. Values of ka' calculated using the Central Jet RTD agree well with values of ka' from literature correlations. There was a linear relationship between ka' and effective Peclet number: ka' = 2.32 x 10(-3) Pe(eff). (C) 2002 Elsevier Science B.V. All rights reserved.

Characterization of Pinus spp. needles by gas chromatography and mass spectrometry: Application to plant-insect interactions

Dissertação apresentada para obtenção do Grau de Doutor em Ciências do Ambiente pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecn

Oxygen mass transfer impact on citric acid production by Yarrowia lipolytica from crude glycerol

Production of citric acid from crude glycerol from biodiesel industry, in batch cultures of Yarrowia lipolytica W29 was performed in a lab-scale stirred tank bioreactor in order to assess the effect of oxygen mass transfer rate in this bioprocess. An empirical correlation was proposed to describe oxygen volumetric mass transfer coefficient (kLa) as a function of operating conditions (stirring speed and specific air flow rate) and cellular density. kLa increased according with a power function with specific power input and superficial gas velocity, and slightly decreased with cellular density. The increase of initial kLa from 7 h-1 to 55 h-1 led to 7.8-fold increase of citric acid final concentration. Experiments were also performed at controlled dissolved oxygen (DO) and citric acid concentration increased with DO up to 60% of saturation. Thus, due to the simpler operation setting an optimal kLa than at controlled DO, it can be concluded that kLa is an adequate parameter for the optimization of citric acid production from crude glycerol by Y. lipolytica and to be considered in bioprocess scale-up. Our empirical correlation, considering the operating conditions and cellular density, will be a valid tool for this purpose.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

On the use of spatially discrete data to compute energy and mass balance

In many practical applications the state of field soils is monitored by recording the evolution of temperature and soil moisture at discrete depths. We theoretically investigate the systematic errors that arise when mass and energy balances are computed directly from these measurements. We show that, even with no measurement or model errors, large residuals might result when finite difference approximations are used to compute fluxes and storage term. To calculate the limits set by the use of spatially discrete measurements on the accuracy of balance closure, we derive an analytical solution to estimate the residual on the basis of the two key parameters: the penetration depth and the distance between the measurements. When the thickness of the control layer for which the balance is computed is comparable to the penetration depth of the forcing (which depends on the thermal diffusivity and on the forcing period) large residuals arise. The residual is also very sensitive to the distance between the measurements, which requires accurately controlling the position of the sensors in field experiments. We also demonstrate that, for the same experimental setup, mass residuals are sensitively larger than the energy residuals due to the nonlinearity of the moisture transport equation. Our analysis suggests that a careful assessment of the systematic mass error introduced by the use of spatially discrete data is required before using fluxes and residuals computed directly from field measurements.

Fate of the herbicide glyphosate and its metabolite AMPA in soils and their transfer to surface waters: A multi-scale approach in the Lavaux vineyards, western Switzerland

The use of herbicides in agriculture may lead to environmental problems, such as surface water pollution, with a potential risk for aquatic organisms. The herbicide glyphosate is the most used active ingredient in the world and in Switzerland. In the Lavaux vineyards it is nearly the only molecule applied. This work aimed at studying its fate in soils and its transfer to surface waters, using a multi-scale approach: from molecular (10-9 m) and microscopic scales (10-6 m), to macroscopic (m) and landscape ones (103 m). First of all, an analytical method was developed for the trace level quantification of this widely used herbicide and its main by-product, aminomethylphosphonic acid (AMPA). Due to their polar nature, their derivatization with 9-fluorenylmethyl chloroformate (FMOC-Cl) was done prior to their concentration and purification by solid phase extraction. They were then analyzed by ultra performance liquid chromatography coupled with tandem mass spectrometry (UPLC-MS/MS). The method was tested in different aqueous matrices with spiking tests and validated for the matrix effect correction in relevant environmental samples. Calibration curves established between 10 and 1000ng/l showed r2 values above 0.989, mean recoveries varied between 86 and 133% and limits of detection and quantification of the method were as low as 5 and 10ng/l respectively. At the parcel scale, two parcels of the Lavaux vineyard area, located near the Lutrive River at 6km to the east of Lausanne, were monitored to assess to which extent glyphosate and AMPA were retained in the soil or exported to surface waters. They were equipped at their bottom with porous ceramic cups and runoff collectors, which allowed retrieving water samples for the growing seasons 2010 and 2011. Results revealed that the mobility of glyphosate and AMPA in the unsaturated zone was likely driven by the precipitation regime and the soil characteristics, such as slope, porosity structure and layer permeability discrepancy. Elevated glyphosate and AMPA concentrations were measured at 60 and 80 cm depth at parcel bottoms, suggesting their infiltration in the upper parts of the parcels and the presence of preferential flow in the studied parcels. Indeed, the succession of rainy days induced the gradual saturation of the soil porosity, leading to rapid infiltration through macropores, as well as surface runoff formation. Furthermore, the presence of more impervious weathered marls at 100 cm depth induced throughflows, the importance of which for the lateral transport of the herbicide molecules was determined by the slope steepness. Important rainfall events (>10 mm/day) were clearly exporting molecules from the soil top layer, as indicated by important concentrations in runoff samples. A mass balance showed that total loss (10-20%) mainly occurred through surface runoff (96%) and, to a minor extent, by throughflows in soils (4%), with subsequent exfiltration to surface waters. Observations made in the Lutrive River revealed interesting details of glyphosate and AMPA dynamics in urbanized landscapes, such as the Lavaux vineyards. Indeed, besides their physical and chemical properties, herbicide dynamics at the catchment level strongly depend on application rates, precipitation regime, land use and also on the presence of drains or constructed channels. Elevated concentrations, up to 4970 ng/l, observed just after the application, confirmed the diffuse export of these compounds from the vineyard area by surface runoff during main rain events. From April to September 2011, a total load of 7.1 kg was calculated, with 85% coming from vineyards and minor urban sources and 15% from arable crops. Small vineyard surfaces could generate high concentrations of herbicides and contribute considerably to the total load calculated at the outlet, due to their steep slopes (~10%). The extrapolated total amount transferred yearly from the Lavaux vineyards to the Lake of Geneva was of 190kg. At the molecular scale, the possible involvement of dissolved organic matter (DOM) in glyphosate and copper transport was studied using UV/Vis fluorescence spectroscopy. Combined with parallel factor (PARAFAC) analysis, this technique allowed characterizing DOM of soil and surface water samples from the studied vineyard area. Glyphosate concentrations were linked to the fulvic-like spectroscopic signature of DOM in soil water samples, as well as to copper, suggesting the formation of ternary complexes. In surface water samples, its concentrations were also correlated to copper ones, but not in a significant way to the fulvic-like signature. Quenching experiments with standards confirmed field tendencies in the laboratory, with a stronger decrease in fluorescence intensity for fulvic-like fluorophore than for more aromatic ones. Lastly, based on maximum concentrations measured in the river, an environmental risk for these compounds was assessed, using laboratory tests and ecotoxicity data from the literature. In our case and with the methodology applied, the risk towards aquatic species was found negligible (RF<1).

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Heterogeneous mass transfer in fluidized beds by computational fluid dynamics

The main objective of this research is to estimate and characterize heterogeneous mass transfer coefficients in bench- and pilot-scale fluidized bed processes by the means of computational fluid dynamics (CFD). A further objective is to benchmark the heterogeneous mass transfer coefficients predicted by fine-grid Eulerian CFD simulations against empirical data presented in the scientific literature. First, a fine-grid two-dimensional Eulerian CFD model with a solid and gas phase has been designed. The model is applied for transient two-dimensional simulations of char combustion in small-scale bubbling and turbulent fluidized beds. The same approach is used to simulate a novel fluidized bed energy conversion process developed for the carbon capture, chemical looping combustion operated with a gaseous fuel. In order to analyze the results of the CFD simulations, two one-dimensional fluidized bed models have been formulated. The single-phase and bubble-emulsion models were applied to derive the average gas-bed and interphase mass transfer coefficients, respectively. In the analysis, the effects of various fluidized bed operation parameters, such as fluidization, velocity, particle and bubble diameter, reactor size, and chemical kinetics, on the heterogeneous mass transfer coefficients in the lower fluidized bed are evaluated extensively. The analysis shows that the fine-grid Eulerian CFD model can predict the heterogeneous mass transfer coefficients quantitatively with acceptable accuracy. Qualitatively, the CFD-based research of fluidized bed process revealed several new scientific results, such as parametrical relationships. The huge variance of seven orders of magnitude within the bed Sherwood numbers presented in the literature could be explained by the change of controlling mechanisms in the overall heterogeneous mass transfer process with the varied process conditions. The research opens new process-specific insights into the reactive fluidized bed processes, such as a strong mass transfer control over heterogeneous reaction rate, a dominance of interphase mass transfer in the fine-particle fluidized beds and a strong chemical kinetic dependence of the average gas-bed mass transfer. The obtained mass transfer coefficients can be applied in fluidized bed models used for various engineering design, reactor scale-up and process research tasks, and they consequently provide an enhanced prediction accuracy of the performance of fluidized bed processes.

Detection and quantification of staphylococcus aureus enterotoxin B in food product using isotopic dilution techniques and mass spectrometry

L’entérotoxine B staphylococcique (SEB) est une toxine entérique hautement résistante à la chaleur et est responsable de plus de 50 % des cas d’intoxication d’origine alimentaire par une entérotoxine. L’objectif principal de ce projet de maîtrise est de développer et valider une méthode basée sur des nouvelles stratégies analytiques permettant la détection et la quantification de SEB dans les matrices alimentaires. Une carte de peptides tryptiques a été produite et 3 peptides tryptiques spécifiques ont été sélectionnés pour servir de peptides témoins à partir des 9 fragments protéolytiques identifiés (couverture de 35 % de la séquence). L’anhydride acétique et la forme deutérée furent utilisés afin de synthétiser des peptides standards marqués avec un isotope léger et lourd. La combinaison de mélanges des deux isotopes à des concentrations molaires différentes fut utilisée afin d’établir la linéarité et les résultats ont démontré que les mesures faites par dilution isotopique combinée au CL-SM/SM respectaient les critères généralement reconnus d’épreuves biologiques avec des valeurs de pente près de 1, des valeurs de R2 supérieure à 0,98 et des coefficients de variation (CV%) inférieurs à 8 %. La précision et l’exactitude de la méthode ont été évaluées à l’aide d’échantillons d’homogénat de viande de poulet dans lesquels SEB a été introduite. SEB a été enrichie à 0,2, 1 et 2 pmol/g. Les résultats analytiques révèlent que la méthode procure une plage d’exactitude de 84,9 à 91,1 %. Dans l’ensemble, les résultats présentés dans ce mémoire démontrent que les méthodes protéomiques peuvent être utilisées efficacement pour détecter et quantifier SEB dans les matrices alimentaires. Mots clés : spectrométrie de masse; marquage isotopique; protéomique quantitative; entérotoxines

Photothermal Characterization of Nanogold Under Conditions of Resonant Excitation and Energy Transfer

We have performed thermal diffusion measurements of nanofluid containing gold and rhodamine 6G dye in various ratios. At certain concentrations, gold is nearly four times more efficient than water in dissipating small temperature fluctuations in a medium, and therefore it will find applications as heat transfer fluids. We have employed dual-beam mode-matched thermal lens technique for the present investigation. It is a sensitive technique in measuring photothermal parameters because of the use of a lowpower, stabilized laser source as the probe. We also present the results of fluorescence measurements of the dye in the nanogold environment.

Strained Silicon on Silicon by Wafer Bonding and Layer Transfer from Relaxed SiGe Buffer

We report the creation of strained silicon on silicon (SSOS) substrate technology. The method uses a relaxed SiGe buffer as a template for inducing tensile strain in a Si layer, which is then bonded to another Si handle wafer. The original Si wafer and the relaxed SiGe buffer are subsequently removed, thereby transferring a strained-Si layer directly to Si substrate without intermediate SiGe or oxide layers. Complete removal of Ge from the structure was confirmed by cross-sectional transmission electron microscopy as well as secondary ion mass spectrometry. A plan-view transmission electron microscopy study of the strained-Si/Si interface reveals that the lattice-mismatch between the layers is accommodated by an orthogonal array of edge dislocations. This misfit dislocation array, which forms upon bonding, is geometrically necessary and has an average spacing of approximately 40nm, in excellent agreement with established dislocation theory. To our knowledge, this is the first study of a chemically homogeneous, yet lattice-mismatched, interface.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Midday auroral breakup events and related energy and momentum transfer from the magnetosheath

Combined observations by meridian-scanning photometers, all-sky auroral TV camera and the EISCAT radar permitted a detailed analysis of the temporal and spatial development of the midday auroral breakup phenomenon and the related ionospheric ion flow pattern within the 71°–75° invariant latitude radar field of view. The radar data revealed dominating northward and westward ion drifts, of magnitudes close to the corresponding velocities of the discrete, transient auroral forms, during the two different events reported here, characterized by IMF |BY/BZ| < 1 and > 2, respectively (IMF BZ between −8 and −3 nT and BY > 0). The spatial scales of the discrete optical events were ∼50 km in latitude by ∼500 km in longitude, and their lifetimes were less than 10 min. Electric potential enhancements with peak values in the 30–50 kV range are inferred along the discrete arc in the IMF |BY/BZ| < 1 case from the optical data and across the latitudinal extent of the radar field of view in the |BY/BZ| > 2 case. Joule heat dissipation rates in the maximum phase of the discrete structures of ∼ 100 ergs cm−2 s−1 (0.1 W m−2) are estimated from the photometer intensities and the ion drift data. These observations combined with the additional characteristics of the events, documented here and in several recent studies (i.e., their quasi-periodic nature, their motion pattern relative to the persistent cusp or cleft auroral arc, the strong relationship with the interplanetary magnetic field and the associated ion drift/E field events and ground magnetic signatures), are considered to be strong evidence in favour of a transient, intermittent reconnection process at the dayside magnetopause and associated energy and momentum transfer to the ionosphere in the polar cusp and cleft regions. The filamentary spatial structure and the spectral characteristics of the optical signature indicate associated localized ˜1-kV potential drops between the magnetopause and the ionosphere during the most intense auroral events. The duration of the events compares well with the predicted characteristic times of momentum transfer to the ionosphere associated with the flux transfer event-related current tubes. It is suggested that, after this 2–10 min interval, the sheath particles can no longer reach the ionosphere down the open flux tube, due to the subsequent super-Alfvénic flow along the magnetopause, conductivities are lower and much less momentum is extracted from the solar wind by the ionosphere. The recurrence time (3–15 min) and the local time distribution (∼0900–1500 MLT) of the dayside auroral breakup events, combined with the above information, indicate the important roles of transient magnetopause reconnection and the polar cusp and cleft regions in the transfer of momentum and energy between the solar wind and the magnetosphere.