Linking temperature estimates and microstructures in deformed polymineralic mantle rocks

To constrain deformation temperatures of mantle shear zones, we studied a strike-slip shear zone (Hilti massif, Semail ophiolite, Oman) and focused on the interaction between microstructural mechanisms and chemical equilibration processes. Quantitative microfabric analysis on harzburgites with different deformation intensity (porphyroclastic tectonite, mylonite, and ultramylonite) was combined with orthopyroxene geothermometry. The average grain size of all phases decreases with decreasing shear zone thickness. Dynamic recrystallization of porphyroclasts in combination with dissolution-precipitation and nucleation result in small-sized, chemically equilibrated pyroxenes. The composition of orthopyroxene was used to calculate deformation temperatures. In the case of the porphyroclastic tectonites, the chemical composition of orthopyroxene has been reset by diffusion yielding temperature estimates of 880-900 degrees C. The mylonites were deformed by dislocation creep of olivine and show a broad range of calculated temperatures, which result from a combination of grain size reduction and inheritance of equilibrium compositions from earlier high-temperature events and diffusion. In mylonites, diffusion profiles combined with geothermometry and grain size analysis indicate a mylonitic deformation temperature of 800-900 degrees C possibly followed by diffusion. In ultramylonites, the smallest grains (<30 mu m) reveal equilibration at temperatures of similar to 700 degrees C during the last stages of ductile deformation, which was dominated by diffusion creep of olivine. Our results provide a crucial link between temperature and evolution of microstructures from dislocation creep to diffusion creep in mantle shear zones.

Spatio-temporal micromeasurements of the oxygen uptake in the developing chick embryo.

A method has been developed for the determination of the oxygen uptake of small areas (0.01 mm2) in an entire chick embryo cultured in vitro under defined metabolic conditions. It is based on the recordings of the spectral changes of the hemoglobin used as oxygen source for the respiring tissue (Barzu and Borza, 1967). Rapid scanning of the hemoglobin absorbance over the preparation allows a comparison of the O2 uptake of various regions. Values of the order of 10(-2) 1 O2 . min-2 are measured in less than 10 sec with a spatial resolution of 100 micron. The differentiation of embryonic tissue is not disturbed by the measurements. The O2 diffusion in the media and in the tissue has been analyzed by digital simulation. The O2 uptake of the Hensen's node was measured from embryos starting at the stage of definitive primitive streak (stage 4) up to the stage of 10 somites. It increases from 0.6 to 1.1 nl . h-1 with a marked acceleration between stages 4 and 5. The values corrected for the protein content of the Hensen's node at stage 4, 5, 6 and 8 are 32, 30 and 28 microliter . mg-1 . h-1 respectively. The first scanning results show different patterns of the O2 utake at the level of the Hensen's node and of the neural plate. At stage 6-7, the corrected O2 uptake is 30 microliter . mg-1 . h-1 for . the former and 43 microliter . mg-1 . h-1 for the latter.

A receptor-like kinase mutant with absent endodermal diffusion barrier displays selective nutrient homeostasis defects.

The endodermis represents the main barrier to extracellular diffusion in plant roots, and it is central to current models of plant nutrient uptake. Despite this, little is known about the genes setting up this endodermal barrier. In this study, we report the identification and characterization of a strong barrier mutant, schengen3 (sgn3). We observe a surprising ability of the mutant to maintain nutrient homeostasis, but demonstrate a major defect in maintaining sufficient levels of the macronutrient potassium. We show that SGN3/GASSHO1 is a receptor-like kinase that is necessary for localizing CASPARIAN STRIP DOMAIN PROTEINS (CASPs)--major players of endodermal differentiation--into an uninterrupted, ring-like domain. SGN3 appears to localize into a broader band, embedding growing CASP microdomains. The discovery of SGN3 strongly advances our ability to interrogate mechanisms of plant nutrient homeostasis and provides a novel actor for localized microdomain formation at the endodermal plasma membrane.

Formation of aluminosilicate-bearing quartz veins in the Simano nappe (Central Alps): structural, thermobarometric and oxygen isotope constraints

We combined structural analysis, thermobarometry and oxygen isotope geochemistry to constrain the evolution of kyanite and/or andalusite-bearing quartz veins from the amphibolite facies metapelites of the Simano nappe, in the Central Alps of Switzerland. The Simano nappe records a complex polyphase tectonic evolution associated with nappe stacking during Tertiary Alpine collision (D1). The second regional deformation phase (132) is responsible for the main penetrative schistosity and mineral lineation, and formed during top-to-the-north thrusting. During the next stage of deformation (D3) the aluminosilicate-bearing veins formed by crystallization in tension gashes, in tectonic shadows of boudins, as well as along shear bands associated with top-to-the-north shearing. D2 and D3 are coeval with the Early Miocene metamorphic peak, characterised by kyanite + staurolite + garnet + biotite assemblages in metapelites. The peak pressure (P) and temperature (T) conditions recorded are constrained by multiple-equilibrium thermobarometry at 630 +/- 20 degrees C and 8.5 +/- 1 kbar (similar to 27 km depth), which is in agreement with oxygen isotope thermometry indicating isotopic equilibration of quartz-kyanite pairs at 670 +/- 50 degrees C. Quartz-kyanite pairs from the aluminosilicate-bearing quartz veins yield equilibration temperatures of 645 +/- 20 degrees C, confirming that the veins formed under conditions near metamorphic peak. Quartz and kyanite from veins and the surrounding metapelites have comparable isotopic compositions. Local intergranular diffusion in the border of the veins controls the mass-transfer and the growth of the product assemblage, inducing local mobilization of SiO2 and Al2O3. Andalusite is absent from the host rocks, but it is common in quartz veins, where it often pseudomorphs kyanite. For andalusite to be stable at T-max, the pressure in the veins must have been substantially lower than lithostatic. An alternative explanation consistent with structural observations would be inheritance by andalusite of the kyanite isotopic signature during polymorphic transformation after the metamorphic peak.

Transport of the organic cation N1-methylnicotinamide by the rabbit proximal tubule. I. Accumulation in the isolated nonperfused tubule.

Isolated nonperfused rabbit renal proximal tubules were used to investigate the basolateral step of transport of the organic cation N1-methylnicotinamide (NMN). NMN accumulation was highest and saturable in S2 and S3 segments, but lowest and nonsaturable in S1 segments. In S1 segments, accumulation of [3H]-NMN (0.5-8 microM in the bath) resulted in an average tubular water/medium concentration ratio (T/M) of 8.2, whereas in S2 and S3 segments T/M averaged 19.5 and 18.6, respectively. At these concentrations, about 30% of the label was attached in all segments to a metabolite comigrating with nicotinamide. KCN (10(-2) M) or ouabain (10(-4) M) reduced T/M to about 8 for all segments. NMN accumulation was inhibited (to a T/M of about 3 with mepiperphenidol) by other organic cations (10(-5)-10(-3) M) with the potency sequence mepiperphenidol greater than tetraethylammonium = quinine greater than morphine, these organic cations having no effect on p-aminohippurate accumulation, except for the highest concentration of quinine (10(-3) M). After correction for metabolism, NMN accumulation could be accounted for by simple electrochemical equilibrium across the basolateral membrane. The basolateral step of NMN transport appears therefore to be a carrier-mediated diffusion, in opposition to the active basolateral accumulation described for tetraethylammonium.

Simple model for nonexponential relaxation in complex fluids

The nonexponential relaxation occurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in any time scale becomes apparent in an effective temperature field, which leads to a hierarchy of relaxation times responsible for the slow relaxation phenomena.

Community structure in mediterranean shallow lentic ecosystems: size-based vs. taxon-based approaches

The main environmental variables determining the community structure and the functioning of Mediterranean shallow lentic ecosystems are described. These ecosystems are characterized by the unpredictability of their water inputs and the high variability in their water level and physical and chemical composition. Variations in flooding, salinity, and water turnover are determinant in species composition and nutrient dynamics. Taxon-based and size-based approaches to the study of the community structure of aquatic organisms that colonise these ecosystems are also compared. The conventional taxonomic approach, based on the determination of species composition, has been used for the identification of patterns in species richness, distribution and temporal dynamics, and for ecological requirements of species and their potential use as ecological indicators. This taxonbased approach has been compared with a size-based approach, where individuals are classified by their size. Size-based approach gives complementary information about community structure and dynamics, especially when communities are dominated by a single species. The use of size diversity combined with species diversity is suggested for a more complete understanding of community structuring in this type of ecosystem. Detailed examples of two Mediterranean shallow lentic ecosystems, the salt marshes of the Empordà wetlands and the Espolla temporary karstic pond, which differ in hydrology and water origin, are used to discuss the suitability of these different approaches

Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond.

The complex structural organization of the white matter of the brain can be depicted in vivo in great detail with advanced diffusion magnetic resonance (MR) imaging schemes. Diffusion MR imaging techniques are increasingly varied, from the simplest and most commonly used technique-the mapping of apparent diffusion coefficient values-to the more complex, such as diffusion tensor imaging, q-ball imaging, diffusion spectrum imaging, and tractography. The type of structural information obtained differs according to the technique used. To fully understand how diffusion MR imaging works, it is helpful to be familiar with the physical principles of water diffusion in the brain and the conceptual basis of each imaging technique. Knowledge of the technique-specific requirements with regard to hardware and acquisition time, as well as the advantages, limitations, and potential interpretation pitfalls of each technique, is especially useful.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Mechanisms of garnet growth in eclogites of the Zermatt-Saas Fee unit, Western Alps

THESIS ABSTRACT Garnets are one of the key metamorphic minerals used to study peak metamorphic conditions or crystallization ages. Equilibrium is typically assumed between the garnet and the matrix. This thesis attempts to understand garnet growth in the Zermatt-Saas Fee (ZSF) eclogites, and discusses consequences for Sm/Nd and Lu/Hf dating and the equilibrium assumption. All studied garnets from the ZSF eclogites are strongly zoned in Mn, Fe, Mg, and Ca. Methods based on chemical zoning patterns and on 3D spatial statistics indicate different growth mechanisms depending on the sample studied. Garnets from the Pfulwe area are grown in a system where surface kinetics likely dominated over intergranular diffusion kinetics. Garnets fram two other localities, Nuarsax and Lago di Cignana, seem to have grown in a system where intergranular diffusion kinetics were dominating over surface kinetics, at least during initial growth. Garnets reveal strong prograde REE+Y zoning. They contain narrow central peaks for Lu + Yb + Tm ± Er and at least one additional small peak towards the rim. The REE Sm + Eu + Gd + Tb ± Dy are depleted in the cores but show one prominent peak close to the rim. It is shown that these patterns cam be explained using a transient matrix diffusion model where REE uptake is limited by diffusion in the matrix surrounding the porphyroblast. The secondary peaks in the garnet profiles are interpreted to reflect thermally activated diffusion due to a temperature increase during prograde metamorphism. The model predicts anomalously low 176Lu/177Hf and 147Sm/144Nd ratios in garnets where growth rates are fast compared to diffusion of the REE, which decreases garnet isochron precisions. The sharp Lu zoning was further used to constrain maximum Lu volume diffusion rates in garnet. The modeled minimum pre-exponential diffusion coefficient which fits the measured central peak is in the order of Do = 5.7* 106 m2/s, taking an activation energy of 270 kJ/mol. The latter was chosen in agreement with experimentally determined values. This can be used to estimate a minimum closure temperature of around 630°C for the ZSF zone. Zoning of REE was combined with published Lu/Hf and Sm/Nd age information to redefine the prograde crystallization interval for Lago di Cignana UHP eclogites. Modeling revealed that a prograde growth interval in the order of 25 m.y. is needed to produce the measured spread in ages. RÉSUMÉ Le grenat est un minéral métamorphique clé pour déterminer les conditions du pic de métamorphisme ainsi que l'âge de cristallisation. L'équilibre entre le grenat et la matrice est requis. Cette étude a pour but de comprendre la croissance du grenat dans les éclogites de la zone de Zermatt-Saas Fee (ZSF) et d'examiner quelques conséquences sur les datations Sm/Nd et Lu/Hf. Tous les grenats des éclogites de ZSF étudiés sont fortement zonés en Mn, Fe, Mg et partiellement en Ca. Les différentes méthodes basées sur le modèle de zonation chimique ainsi que sur les statistiques de répartition spatiale en 3D indiquent un mécanisme de croissance différent en fonction de la localité d'échantillonnage. Les grenats provenant de la zone de Pfulwe ont probablement crû dans un système principalement dominé par la cinétique de surface au détriment de 1a cinétique de diffusion intergranulaire. Les grenats provenant de deux autres localités, Nuarsax et Lago di Cignana, semblent avoir cristallisé dans un système dominé par la diffusion intergranulaire, au moins durant les premiers stades de croissance. Les grenats montrent une forte zonation prograde en Terres Rares (REE) ainsi qu'en Y. Les profils présentent au coeur un pic étroit en Lu + Yb+ Tm ± Er et au moins un petit pic supplémentaire vers le bord. Les coeurs des grenats sont appauvris en Sm + Eu + Gd + Tb ± Dy, mais les bords sont marqués par un pic important de ces REE. Ces profils s'expliquent par un modèle de diffusion matricielle dans lequel l'apport en REE est limité par la diffusion dans la matrice environnant les porphyroblastes. Les pics secondaires en bordure de grain reflètent la diffusion activée par l'augmentation de la température lors du métamorphisme prograde. Ce modèle prédit des rapports 176Lu/177Hf et 147Sm/144Nd anormalement bas lorsque les taux de croissance sont plus rapides que la diffusion des REE, ce qui diminue la précision des isochrones impliquant le grenat. La zonation nette en Lu a permis de contraindre le maximum de diffusion volumique par une approche numérique. Le coefficient de diffusion minimum modélisé en adéquation avec les pics mesurés est de l'ordre de Do = 5.7*10-6 m2/s, en prenant une énergie d'activation ~270 kJ/mol déterminée expérimentalement. Ainsi, la température de clôture minimale est estimée aux alentours de 630°C pour la zone ZSF. Des nouvelles données de zonation de REE sont combinées aux âges obtenus avec les rapports Lu/Hf et Sm/Nd qui redéfissent l'intervalle de cristallisation prograde pour les éclogites UHP de Lago di Cignana. La modélisation permet d'attribuer au minimum un intervalle de croissance prograde de 25 Ma afin d'obtenir les âges préalablement mesurés. RESUME GRAND PUBLIC L'un des principaux buts du pétrologue .métamorphique est d'extraire des roches les informations sur l'évolution temporelle, thermique et barométrique qu'elles ont subi au cours de la formation d'une chaîne de montagne. Le grenat est l'un des minéraux clés dans une grande variété de roches métamorphiques. Il a fait l'objet de nombreuses études dans des terrains d'origines variées ou lors d'études expérimentales afin de comprendre ses domaines de stabilité, ses réactions et sa coexistence avec d'autres minéraux. Cela fait du grenat l'un des minéraux les plus attractifs pour la datation des roches. Cependant, lorsqu'on l'utilise pour la datation et/ou pour la géothermobarométrie, on suppose toujours que le grenat croît en équilibre avec les phases coexistantes de la matrice. Pourtant, la croissance d'un minéral est en général liée au processus de déséquilibre. Cette étude a pour but de comprendre comment croît le grenat dans les éclogites de Zermatt - Saas Fee et donc d'évaluer le degré de déséquilibre. Il s'agit aussi d'expliquer les différences d'âges obtenues grâce aux grenats dans les différentes localités de l'unité de Zermatt-Saas Fee. La principale question posée lors de l'étude des mécanismes de croissance du grenat est: Parmi les processus en jeu lors de la croissance du grenat (dissolution des anciens minéraux, transport des éléments vers le nouveau grenat, précipitation d'une nouvelle couche en surface du minéral), lequel est le plus lent et ainsi détermine le degré de déséquilibre? En effet, les grenats d'une des localités (Pfulwe) indiquent que le phénomène d'adhérence en surface est le plus lent, contrairement aux grenats des autres localités (Lago di Cignana, Nuarsax) dans lesquels ce sont les processus de transport qui sont les plus lents. Cela montre que les processus dominants sont variables, même dans des roches similaires de la même unité tectonique. Ceci implique que les processus doivent être déterminés individuellement pour chaque roche afin d'évaluer le degré de déséquilibre du grenat dans la roche. Tous les grenats analysés présentent au coeur une forte concentration de Terres Rares: Lu + Yb + Tm ± Er qui décroît vers le bord du grain. Inversement, les Terres Rares Sm + Eu + Gd + Tb ± Dy sont appauvries au coeur et se concentrent en bordure du grain. La modélisation révèle que ces profils sont-dus à des cinétiques lentes de transport des Terres Rares. De plus, les modèles prédisent des concentrations basses en éléments radiogéniques pères dans certaines roches, ce qui influence fortement sur la précision des âges obtenus par la méthode d'isochrone. Ceci signifie que les roches les plus adaptées pour les datations ne doivent contenir ni beaucoup de grenat ni de très gros cristaux, car dans ce cas, la compétition des éléments entre les cristaux limite à de faibles concentrations la quantité d'éléments pères dans chaque cristal.

Plutonium and americium isotopes as alternative chronostratigraphic markers in tropical regions: An application in the Havana Bay (Cuba)

The low 137Cs activity observed in marine sediments of tropical regions often precludes its use as chronostratigraphic marker. Here we present a study on the use of Pu and Am radioisotopes as alternative markers to constrain the 210Pb ages in a sediment core of the Havana Bay (Cuba). Mean activity ratios of 238Pu/239,240Pu, 241Am/239,240Pu and 241Pu/239,240Pu indicated that the nuclear weapon tests fallout is the main source of the anthropogenic radionuclides. While the inventory of 137Cs in the sediments is lower than the expected fallout inventory, 239,240Pu accumulates in the sediments with inventories higher than the expected fallout inventory. The high fluxes of 239,240Pu are nevertheless corroborated here through use of 210Pb, and confirm that focusing of solid particles is of great importance in the investigated site. 239,240Pu showed to be a useful time tracer in marine sites where the 137Cs signal is very low.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Mass transfer and particleinteractions in granular systems and suspension flows

The purpose of this study was to investigate some important features of granular flows and suspension flows by computational simulation methods. Granular materials have been considered as an independent state ofmatter because of their complex behaviors. They sometimes behave like a solid, sometimes like a fluid, and sometimes can contain both phases in equilibrium. The computer simulation of dense shear granular flows of monodisperse, spherical particles shows that the collisional model of contacts yields the coexistence of solid and fluid phases while the frictional model represents a uniform flow of fluid phase. However, a comparison between the stress signals from the simulations and experiments revealed that the collisional model would result a proper match with the experimental evidences. Although the effect of gravity is found to beimportant in sedimentation of solid part, the stick-slip behavior associated with the collisional model looks more similar to that of experiments. The mathematical formulations based on the kinetic theory have been derived for the moderatesolid volume fractions with the assumption of the homogeneity of flow. In orderto make some simulations which can provide such an ideal flow, the simulation of unbounded granular shear flows was performed. Therefore, the homogeneous flow properties could be achieved in the moderate solid volume fractions. A new algorithm, namely the nonequilibrium approach was introduced to show the features of self-diffusion in the granular flows. Using this algorithm a one way flow can beextracted from the entire flow, which not only provides a straightforward calculation of self-diffusion coefficient but also can qualitatively determine the deviation of self-diffusion from the linear law at some regions nearby the wall inbounded flows. Anyhow, the average lateral self-diffusion coefficient, which was calculated by the aforementioned method, showed a desirable agreement with thepredictions of kinetic theory formulation. In the continuation of computer simulation of shear granular flows, some numerical and theoretical investigations were carried out on mass transfer and particle interactions in particulate flows. In this context, the boundary element method and its combination with the spectral method using the special capabilities of wavelets have been introduced as theefficient numerical methods to solve the governing equations of mass transfer in particulate flows. A theoretical formulation of fluid dispersivity in suspension flows revealed that the fluid dispersivity depends upon the fluid properties and particle parameters as well as the fluid-particle and particle-particle interactions.

Predicting diffusion of innovations with self-organisation and machine learning

The main subject of this master's thesis was predicting diffusion of innovations. The prediction was done in a special case: product has been available in some countries, and based on its diffusion in those countries the prediction is done for other countries. The prediction was based on finding similar countries with Self-Organizing Map~(SOM), using parameters of countries. Parameters included various economical and social key figures. SOM was optimised for different products using two different methods: (a) by adding diffusion information of products to the country parameters, and (b) by weighting the country parameters based on their importance for the diffusion of different products. A novel method using Differential Evolution (DE) was developed to solve the latter, highly non-linear optimisation problem. Results were fairly good. The prediction method seems to be on a solid theoretical foundation. The results based on country data were good. Instead, optimisation for different products did not generally offer clear benefit, but in some cases the improvement was clearly noticeable. The weights found for the parameters of the countries with the developed SOM optimisation method were interesting, and most of them could be explained by properties of the products.