Quantum mechanical potential surfaces and calculations on minerals and molecular clusters

Recently, ab-initio quantum mechanical potential surfaces calculated for silicate hydroxyacid molecules were used to extract covalent potentials for use in mineral physics calculations (Lasaga and Gibbs 1987). The calculations showed that these potentials are capable of generating the structure and physical properties of silicate minerals. In this paper we explore in more detail the suitability of various covalent potentials in mimicking the topography of the ab-initio potential surfaces. We also extend the use of such quantum-derived potentials in generating the structures of hydroxyacid dimers, trimers, and pentamers of silicate tetrahedra and in studying the structure and the dynamical properties of minerals and glasses.     

Seismic Q for the lithosphere of the Montenegro region (Yugoslavia): frequency,depth and time windowing effects

The availability of accelerometric data for the Montenegro earthquake of 15th April 1979 makes it possible to investigate seismic Q of the lithosphere in that region, in particular, its dependence on frequency, on the depth reached by seismic waves, and on the length of time windows in which signals are processed. Two different spectral methods, S phase energy ratio and coda envelope decay, are applied, respectively, to direct and scattered shear waves. Similar results are obtained using different portions of the recordings, i.e., coda waves for the envelope decay fit and the S wave train, with a significant duration of ～ 10 s, for the energy ratios. The same apparent Q (Q ～ 40 f, where f is the frequency expressed in Hz) that is found for other neighbouring central Mediterranean regions (e.g., Ancona, on the central Italian Adriatic coast; Valnerina, in the central Apennines; Irpinia, in the southern Apennines) is also found for the southern Yugoslavian coast, in the band 1–25 Hz up to a maximum range of ～ 120 km from the focus. This strong frequency dependence is probably connected with the type of small-scale heterogeneity and the same geological age and level of tectonic activity peculiar to all these seismotectonic areas.In order to compare the apparent Q of the whole S wave train, ～ 10 s long, with the (intrinsic) apparent Q of the single direct S wave (usually 1 s or less), the maximum entropy method is applied in the energy spectrum computation for shorter wave trains. The use of shorter time windows does not reveal any significant variation in the tendency of Q to increase linearly with frequency as the length of the time window containing the sample of the S waves decreases. This seems to indicate that scattering-dependent Q is generally inseparable from intrinsic Q in the lithosphere when estimates based on variations with distance of the seismic signal spectrum are used. While the type of linear growth with frequency does not seem to undergo any variations (it remains of the Q = qf type), the data show there are a considerable decrease in the coefficient of proportionality Q with decreasing duration of the window of S waves analysed, probably as a result of variations in seismic attenuation with depth.     

Kinetics of reactions between aqueous sulfates and sulfides in hydrothermal systems

The rates of chemical reactions between aqueous sulfates and sulfides are essentially identical to sulfur isotopic exchange rates between them, because both the chemical and isotopic reactions involve simultaneous oxidation of sulfide-sulfur atoms and reduction of sulfate-sulfur. The rate of reaction can be expressed as a second order rate law: R = k·[∑SO₄^2?]·[∑S^2?], where R is the overall rate, k is the rate constant and [∑SO₄^2?] and [∑S^2?] are molal concentrations. We have computed the rate constants from the available experimental data on the partial exchange of sulfur isotopes between aqueous sulfates and sulfides using the rate law established by us: $\text{ln(}\text{α}{}^{\mathrm{e}}\text{? α}\text{α}{}^{\mathrm{e}}\text{? α}{}^0\text{) = ? kt([∑SO}{}_4{}^{\mathrm{2?}}\text{] + [∑S}{}^{\mathrm{2?}}\text{])}$, where t is time and α⁰, α, and α^e are, respectively, the fractionation factors at t = 0 (the initial condition), at the end of experiment, and at equilibrium. The equilibrium fractionation factor can be expressed as: $\text{1000 ln α}{}^{\mathrm{e}}\text{=}\text{6.463 × 10}{}^6\text{T}{}^2\text{+ 0.56 (±.5)}$ (T in Kelvin).The rate constants are strongly dependent on T and pH, but not in as simple a manner as suggested by Igumnov (1976). Our rate constants in Na-bearing hydrothermal solutions decrease by 1 order of magnitude with an increase in pH by 1 unit at pH's less than ~3, remain constant in the pH range of ~4 to ~7, and again decrease at pH >7. The activation energy for the reaction also depends on pH: 18.4 ± 1 kcal/mole at pH = 2, 29.6 ± 1 kcal/mole at pH = 4 to 7, and between 40 and 47 kcal/mole at pH around 9. The observed pH dependence of the rate constant and of the activation energy can be best explained by a model involving thiosulfate molecules as reaction intermediates, in which the intramolecular exchange of sulfur atoms in thiosulfates becomes the rate determining step.The rate constants obtained in this study were used to compute the changes in the isotopic fractionation factors between aqueous sulfates and sulfides during cooling of fluids. Comparisons with data of coexisting sulfate-sulfide minerals in hydrothermal deposits, suggest that simple cooling was not a likely mechanism for coprecipitation of sulfate and sulfide minerals at temperatures below 350°C. Mixing of sulfide-rich solutions with sulfate-rich solutions at or near the depositional sites is a more reasonable process for explaining the observed fractionation.The degree of attainment of chemical equilibrium between aqueous sulfates and sulfides in a hydrothermal system, and the applicability of a_O2-pH type diagrams to mineral deposits, depends on the ∑S content and the thermal history of the fluid, which in turn is controlled by the flow rate and the thermal gradient in the system.The rates of sulfate reduction by non-bacterial processes involving a variety of reductants are also dependent on T, pH, [∑SO₄^2?], and [∑S^2?], and appear to be fast enough to become geochemically important at temperatures above about 200°C.     

Granulite-amphibolite facies metasediments from the Serre (Calabria,Southern Italy): their protoliths and the processes controlling their chemistry

In the northwestern Serre, a near continuous section through the Palaeozoic lower continental crust crops out. This paper deals with granulite facies metasedimentary rocks of this section. Fifty-five chemical analyses (major elements, Sc, V, Cr, Co, Ni, Rb, Sr, Y, Nb and Ba) are given. Chemical data indicate that the original sedimentary sequence was made up of arenites in the lower part and mainly Fe and Mg rich pelites in the upper part. The metapelites experienced anatexis and removal of some melt, whereas the meta-arenites suffered only incipient anatexis and became dehydration granulites. The various rock types display an overall relatively low K/Rb ratio due mainly to the stability of K- and Rb-retaining phases. A weighted mean composition of the fragment of the lower continental crust outcropping in the Serre has been established by integrating the chemical data for metasediments (55 analyses), metabasites (92 analyses) and dioritic and tonalitic gneisses (10 analyses) with the field data. This composition compared to the compositions of the bulk continental crust and of other sections considered as belonging to the lower crust, confirms the hypothesis that (1) the lower crust is heterogeneous, and (2) it is more basic than the continental crust.     

Analysis of the weightiness of site effects on reinforced concrete (RC) building seismic behaviour: The Adra town example (SE Spain)

The damage distribution in Adra town (south‐eastern Spain) during the 1993 and 1994 Adra earthquakes (5.0 magnitude), that reached a maximum intensity degree of VII (European Macroseismic Scale (EMS scale)), was concentrated mainly in the south‐east zone of the town and the most relevant damage occurred in reinforced concrete (RC) buildings with four or five storeys. In order to evaluate the influence of ground condition on RC building behaviour, geological, geomorphological and geophysical surveys were carried out, and a detailed map of ground surface structure was obtained. Short‐period microtremor observations were performed in 160 sites on a 100m × 100m dimension grid and Nakamura's method was applied in order to determine a distribution map of soil predominant periods. Shorter predominant periods (0.1–0.3 s) were found in mountainous and neighbouring zones and larger periods (greater than 0.5 s) in thicker Holocene alluvial fans. A relationship T = (0.049 ± 0.001)N, where T is the natural period of swaying motion and N is the number of storeys, has been empirically obtained by using microtremor measurements at the top of 38 RC buildings (ranging from 2 to 9 storeys). 1‐D simulation of strong motion on different soil conditions and for several typical RC buildings were computed, using the acceleration record in Adra town of the 1993 earthquake. It is noteworthy that all the aforementioned results show the influence of site effects in the degree and distribution of observed building damage. Copyright © 2007 John Wiley & Sons, Ltd.     

Relations entre le creusement et le comblement des perturbations et leur déplacement

Résumé On commence par définir le creusement et le comblement d'une fonctionp(, t) du tempst et des points (, ) d'une surface régulière fermée en se donnant, sur cette surface, un vecteur vitesse d'advection ou de transfert tangent à . Le creusement (ou le comblement) est la variation dep sur les particules fictives se déplaçant constamment et partout à la vitesse , A chaque vecteur et pour un mêmep(, ,t) correspond naturellement une fonction creusementC (, ,t) admissible a priori; mais une condition analytique très générale (l'intégrale du creusement sur toute la surface fermée du champ est nulle à chaque instant), à laquelle satisfont les fonctions de perturbation sur les surfaces géopotentielles, permet de restreindre beaucoup la généralité des vecteurs d'advection admissibles a priori et conduit à des vecteurs de la forme: , oùT est un scalaire régulier, () une fonction régulière de la latitude , le vecteur unitaire des verticales ascendantes etR/2 une constante. Ces vecteurs sont donc une généralisation naturelle des vitesses géostrophiques attachées à tout scalaire régulier. Dans le cas oùp(, ,t) est la perturbation de la pression sur la surface du géoïde, le vecteur d'advection par rapport auquel on doit définir le creusement est précisément une vitesse géostrophique: on a alors ()=sin etT un certain champ bien défini de température moyenne.On déduit ensuite une formule générale de géométrie et de cinématique différentielles reliant la vitesse de déplacement d'un centre ou d'un col d'un champp(, ,t) à son champ de creusementC (, ,t) et au vecteur d'advection correspondant. Cette formule peut être transformée et prend la forme d'une relation générale entre le creusement (ou le comblement) d'un centre ou d'un col et la vitesse de son déplacement, sans que le vecteur d'advection intervienne explicitement. On analyse alors les conséquences de ces formules dans les cas suivants: 1^o) perturbations circulaires dans le voisinage du centre; 2^o) perturbations ayant, dans le voisinage du centre, un axe de symétrie normal ou tangent à la vitesse du centre; 3^o) évolution normale des cyclones tropicaux.Finalement, on examine les relations qui existent entre le creusement ou le comblement d'un champ, le vecteur d'advection et la configuration des iso-lignes du champ dans le voisinage d'un centre.Ces considérations permettent d'expliquer plusieurs propriétés bien connues du comportement des perturbations dans différentes régions.

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Summary The deepening and filling (development) of a functionp(, ,t) of the timet and the points (, ) of a regular closed surface is first of all defined, in respect to a given advection or transfer velocity field tangent to , as the variation ofp on any fictitious particle moving constantly and everywhere with the velocity . For a givenp(, ,t) and to any there corresponds a well defined development fieldC (, ,t). All theseC fields are a priori admissible, but a very general analytical condition of the perturbation fields in synoptic meteorology (the integral of the development fieldC (, ,t) on any geopotential surface vanishes at any moment), leads to an important restriction to advection vectors of the form: , whereT is any regular scalar, () any regular function of latitude, the unit vector of the ascending verticals andR/2 a constant. These vectors are a natural generalisation of the geostrophic velocities attached to any regular scalar. Whenp(, ,t) is the pressure perturbation at sea level, its development must be defined in respect to a geostrophic advection vector belonging to the above defined class of vectors with ()=sin andT a well defined mean temperature field.A general formula of the differential geometry and kinematics ofp(, ,t) is then derived, giving the velocity of any centre and col of ap(, ,t) as a function of the advection vector and the corresponding development fieldC (, ,t). This formula can be transformed and takes the form of a general relation between the deepening (and filling) of a centre (or a col) of ap(, ,t) and its displament velocity, the advection vector appearing no more explicitly. A detailed analysis of the consequences of these formulae is then given for the following cases: 1^o) circular perturbations in the vicinity of a centre; 2^o) perturbations having, in the vicinity of a centre, an axis of symmetry normal or tangent to the velocity of the centre; 3^o) normal evolution of the tropical cyclones.Finally, the relations between the developmentC (, ,t) of a fieldp(, ,t), the advection velocity vector and the configuration of the iso-lines in the vicinity of a centre are analysed.These theoretical results give a rational explanation of several well known properties of the behaviour of the perturbations in different geographical regions.

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Communication à la 2ème Assemblée de la «Società Italiana di Geofisica e Meteorologia» (Gênes, 23–25 Avril 1954).     

Sur la prévision des perturbations atmosphériques

Résumé Le mémoire commence par une analyse des relations qui existent entre les notions d'analyticité, de non analyticité et d'unicité des solutions d'équations d'évolution d'un certain type et les notions de déterminisme, d'indéterminisme et de prédéterminabilité des phénomènes correspondants.Ces résultats sont ensuite appliqués au cas des perturbations atmosphériques et l'on montre, en s'appuyant sur la théorie des distributions, que les solutions d'une équation différentielle spatio-temporelle de ces perturbations, déduite par l'auteur dans des mémoires antérieurs, jouissent de la propriété d'unicité, ce qui justifié théoriquement l'application de cette équation en prévision du temps.Finalement, ou expose brièvement un nouveau procédé permettant une détermination facile du facteur de non-analyticité qui intervient dans la solution générale de l'équation des perturbations.

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Summary The paper begins with an analysis of the relations existing between the notions of analyticity, non-analyticity and unicity of the solutions of equations of evolution of a certain type and the notions of determinism, indeterminism and predeterminability of the corresponding phenomena.These results are then applied to the atmospheric perturbations and it is shown, by means of the distribution theory, that the solutions of a spatio-temporal differential equation of these perturbations, previously deduced by the author in other papers, have the unicity property. This is the theoretical proof that such equation can be applied in weather forecasting.Finally, a new procedure is outlined for an easy determination of the non-analyticity factor appearing in the general solution of the perturbation equation.

     

Invariant Tori in the Secular Motions of the Three-body Planetary Systems

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter–Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.     

Homogeneity of the Geochemical Reference Material BRP-1 (Paraná Basin Basalt) and Assessment of Minimum Mass

Reference materials (RM) are required for quantitative analyses and their successful use is associated with the degree of homogeneity, and the traceability and confidence limits of the values established by characterisation. During the production of a RM, the chemical characterisation can only commence after it has been demonstrated that the material has the required level of homogeneity. Here we describe the preparation of BRP-1, a proposed geochemical reference material, and the results of the tests to evaluate its degree of homogeneity between and within bottles. BRP-1 is the first of two geochemical RM being produced by Brazilian institutions in collaboration with the United States Geological Survey (USGS) and the International Association of Geoanalysts (IAG). Two test portions of twenty bottles of BRP-1 were analysed by wavelength dispersive-XRF spectrometry and major, minor and eighteen trace elements were determined. The results show that for most of the investigated elements, the units of BRP-1 were homogeneous at conditions approximately three times more rigorous than those strived for by the test of "sufficient homogeneity". Furthermore, the within bottle homogeneity of BRP-1 was evaluated using small beam (1 mm²) synchrotron radiation XRF spectrometry and, for comparison, the USGS reference materials BCR-2 and GSP-2 were also evaluated. From our data, it has been possible to assign representative minimum masses for some major constituents (1 mg) and for some trace elements (1-13 mg), except Zr in GSP-2, for which test portions of 74 mg are recommended.