Trace element geochemistry and isotopy (Sm, Nd) of lamproites of the Aldan Shield

<p>Lamproites of the Aldan Shield were found (Vladykin 1985) at the beginning of 80-es (for the first time in the USSR), being mainly the intrusive varieties of lamproites, though there occur among them some dyke and volcanic varieties. The general geological and geochemical features of lamproites of the Aldan shield were reported at the VI International Kimberlite Conference at Novosibirsk in 1995 (Vladykin 19971).</p><p>In  Aldan Shield there are known 14 locations of lamproites mostly referred to the Mesozoic rifting. This zone stretches out over all Aldan Shield, from the Murun massif in the Western part of the shield up to the Konder massif in the Eastern part of the shield. These occurrences of lamproites are of Jurassic age (120-150 m.a.). Only lamproites of Khani massif in the SW part of the Aldan Shield are more ancient. At first (according to the data of V.V.Arkhangelskaya) the Khani massif was considered to be Paleozoic, then using K-Ar method (VSEGEI) it was established Proterozoic age of biotite pyroxenites of the massif 1800 m.a. We found the dyke of olivine lamproites of the massif that crosses the biotite pyroxenites. We obtained even more ancient age – 2700 m.a. by zircons from these lamproites with a device SHRIMP (VSEGEI) (Vladykin, Lepekhina - 2005).</p><p>New data on Sr-Nd – systematization of the lamproites of the Aldan Shield have been obtained. The ratios 87Sr/86Sr in lamproites of Aldan vary from 0.703 to 0.708, whereas έ Nd – from -6 to -25. The source of Aldan Shield lamproites is enriched mantle ЕМ-1 (рис.1), that is consistent with their geological position (Vladykin -1997). They are situated between the Aldan Shield and the Siberian platform, where did not occur subduction. The North American lamproites (Leucite Hills, Smoky Bewt, Prery Creak ecc) have a similar position between the Canadian shield and the North-American platform and the same mantle source.</p><p>Compared to the Australian lamproites, the lamproites of the Aldan Shield have lower concentrations of rare-earth elements. The TR spectra for the Aldan lamproites (fig. 2) are rather uniform. A slight slope of the spectrum curves and slight Eu-anomaly are typical. For the earlier olivine lamproites lower TR concentrations are typical as compared with more differentiated leucite and sanidine lamproites.</p><p>The lamproites of the Aldan Shield originated from the enriched mantle source ЕМ-1, the age of that, according to Pb isotopic data, obtained for the rocks of the Murun massif (Vladykin 19972) is estimated as 3200 m.a. The dykes of the olivine lamproites of the Khani massif are the oldest lamproites in the world (2700 m.a.). The TR spectrum of the same type is indicative of similar genesis of the lamproites from various massifs of the Aldan Shield. In spite of the deep mantle source of the Aldan lamproites, they don’t bear diamonds actually, since the diamonds were likely burnt during their crystallization (at t- 1200-1000o C).</p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gepj.68d9d1da710063179070161/sdaolpUECMynit/12UGE&app=m&a=0&c=833cbfbac13f62c9a0cf1376ced7de51&ct=x&pn=gepj.elif&d=1" alt=""></p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.52e855ea710063379070161/sdaolpUECMynit/12UGE&app=m&a=0&c=1874a7ee7bd883faf28c1a71fad727e1&ct=x&pn=gnp.elif&d=1" alt=""></p><p>RFBR 09-05-00116, 08-05-9000.</p><p>References:</p><p>Vladykin N.V. First occurence of lamproites in the USSR.//Doklady Academii Nauk SSSR, 1985, Vol..208, N 3, p.718-722. (in Russia).</p>

Sequence selection properties in Cp (X) with the double ideals

Recently Bukovský, Das and Šupina [Ideal quasi-normal convergence and related notions, Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) of Cp (X) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω, which are motivated by Arkhangeľskii local αi -properties [The frequency spectrum of a topological space and the classification of spaces, Dokl. Akad. Nauk SSSR 13 (1972), 1185–1189]. In this paper, we obtain some characterizations of (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) properties of Cp (X) in the terms of covering properties and selection principles. Under certain conditions on ideals 𝓘 and 𝓙, we identify the minimal cardinalities of a space X for which Cp (X) does not have (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) properties.

Direct Observation of Deviations from Taylor's Frozen Hypothesis and Scaling Laws in Canonical Jet Flows

The legendary difficulties in studying turbulent flows stem, in part, from the lack of high-frequency, high-resolution measurements to interrogate small-scale structures and their rapid evolution. Our experiments, employing a burst-mode laser system, capture both spatially resolved velocity fields and their dynamics using high-resolution particle image velocimetry measurements at 100 kHz. We show directly that fluctuations of flow velocity in an axisymmetric jet flow are inhomogeneous and anisotropic. The velocity of the peak of the time-delayed cross correlation function C(r, r 0 ; τ ) is smaller than the convection velocity; thus Taylor’s frozen hypothesis [Taylor GI, Proc. R. Soc. London, Ser A 164, 476 (1938)] fails to generalize for inhomogeneous jet flows, consistent with prior studies. Its peak decays exponentially in time. Second, the structure functions are found to be isotropic at small distances, but not at large distances. Extended self-similarity is found to hold [Benzi R et al., Physics Review E 48, R29 (1993)], but no inertial range is found where the Kolmogorov 2 3 -law [Kolmogorov AN, Dokl. Akad. Naud. SSSR 30, 299 (1941)] holds. Spectral-energy density of the jet flow, although anisotropic, is consistent with the Kolmogorov-Obukhov 5 3 -law [Obukhov AM, Izvestiya Akad. Nauk. SSSR 32, 19 (1941)] in the flow direction.

T-x-диаграмма системы Ga – Se в диапазоне составов 48.0 – 61.5 мол. % Se по данным термического анализа

Целью настоящей работы было термографическое исследование T-x диаграммы системы Ga – Se в диапазоне температур от 500 до 1100 °С и в диапазоне составов от 48.0 до 61.5 mol % Se. Методом исследования являлся дифференциальный термический анализ c компьютерной регистрацией данных. Получены свидетельства о наличии ретроградного солидуса фазы g-GaSe со стороны селена (с областью гомогенности в несколько десятых mol % при температурах выше эвтектической) и о независимом существовании близких по составу фаз e-GaSe и g-GaSe. При этом более богатая галлием фаза e-GaSe испытывает перитектический распад с образованием расплава (L2) и g-GaSe. Для темпера-туры предполагаемой перитектической реакции получено значение 921 ±2 °С. Вместе стем, на данном этапе работ не получено никаких данных в пользу существования ожидавшейся (по аналогии с системой Ga – S) высокотемпературной модификации, близкой по составу к сесквиселениду галлия (Ga2S3). Другие результаты, полученные в настоящей работе (характер и температуры плавления промежуточных фаз, температуры эвтектического и монотектического превращений, а также координата эвтектического состава), хорошо согласуются с литературными данными по исследованной системе ЛИТЕРАТУРА1. Kainzbauer P., Richter K. W., Ipser H. The binary Bi-Rh phase diagram: stable and metastable phases //J. Phase Equilibria and Diffusion, 2018, v. 39(1), pp. 17– 34. DOI: https://doi.org/10.1007/s11669-017-0600-52. Dolyniuk J.-A., Kaseman D. C., Sen S., Zhao J., Osterloh F. E., Kovnir K. mP-BaP3: A new phase froman old binary system // Chem. Eur. J., 2014, v. 20, pp. 10829–10837, DOI: https://doi.org/10.1002/chem.2013050783. Березин С. С., Завражнов А. Ю., Наумов А. В., Некрылов И. Н., Брежнев Н. Ю. Фазовая диаграммасистемы Ga–S в области 48.0–60.7 мол. % S // Конденсированные среды и межфазные границы, 2017,т. 19(3), с. 321–335. DOI: https://doi.org/10.17308/kcmf.2017.19/2084. Волков В. В., Сидей В. И., Наумов А. В., Некрылов И. Н., Брежнев Н. Ю., Малыгина Е. Н., Завражнов А. Ю. Высокотемпературная кубическая модификация сульфида галлия (Xs = 59 мол. %) и Т, х-диаграмма системы Ga – S // Конденсированные среды и межфазные границы, 2019, т. 21(1), с. 37–50.DOI: https://doi.org/10.17308/kcmf.2019.21/7155. Zavrazhnov A., Berezin S., Kosyakov A., Naumov A., Berezina M., Brezhnev N. J. The phase diagramof the Ga–S system in the concentration range of 48.0–60.7 mol % S // Thermal Analysis and Calorimetry,2018, v. 134(1), pp. 483–492. DOI: https://doi.org/10.1007/s10973-018-7124-z6. Okamoto H. Ga–Se (Gallium-Selenium) // J. Phase Equilibria and Diffusion, 2009, v. 30, p. 658. DOI:https://doi.org/10.1007/s11669-009-9601-37. Dieleman J., Sanders F. H. M. Phase diagram of the Ga-Se system // Phillips J. Res., 1982, v. 37(4),pp. 204 – 229.8. Zavrazhnov A. Yu. Turchen D. N., Goncharov Eu. G., Zlomanov V. P. Manometric method for thestudy of P-T-x diagrams // J. Phase Equilibria and Diffusion, 2001, v. 22(4), pp. 482–490. DOI: https://doi.org/10.1361/1054971017703330639. Shtanov V. I, Komov A. A, Tamm M. E., Atrashenko D. V., Zlomanov V. P. Gallium-selenium systemphase diagram and photoluminescence spectra of GaSe crystals // Doklady Akademii nauk SSSR, 1998, v. 361(3),pp. 357–361. (in Russ.)10. Glazov V. M., Pavlova L. M. Semiconductor and metal binary systems. Phase equilibria and chemicalthermodynamics. Springer, 1989, 327 p. DOI: https://doi.org/10.1007/978-1-4684-1680-011. Ider M. Pankajavalli R., Zhuang W. Thermochemistry of the Ga–Se System. J. Solid State Scienceand Techn., 2015, v. 4(5), Q51–Q60 DOI: https://doi.org/10.1149/2.0011507jss12. Zavrazhnov A., Naumov A., Sidey V., Pervov V. Composition control of low-volatile solids throughchemical vapor transport reactions. III. The example of gallium monoselenide: Control of the polytypicstructure, non-stoichiometry and properties // Thermochimica Acta, 2012, v. 527, pp. 118–124. DOI:https://doi.org/10.1016/j.tca.2011.10.012

Revisiting Bolgiano–Obukhov scaling for moderately stably stratified turbulence

According to the celebrated Bolgiano–Obukhov (Bolgiano, J. Geophys. Res., vol. 64 (12), 1959, pp. 2226–2229; Obukhov, Dokl. Akad. Nauk SSSR, vol. 125, 1959, p. 1246) phenomenology for moderately stably stratified turbulence, the energy spectrum in the inertial range shows a dual scaling: the kinetic energy follows (i) ${\sim}k^{-11/5}$ for $k<k_{B}$, and (ii) ${\sim}k^{-5/3}$ for $k>k_{B}$, where $k_{B}$ is the Bolgiano wavenumber. The $k^{-5/3}$ scaling, akin to passive scalar turbulence, is a direct consequence of the assumption that buoyancy is insignificant for $k>k_{B}$. We revisit this assumption, and using the constancy of kinetic and potential energy fluxes and simple theoretical analysis, we find that the $k^{-5/3}$ spectrum is absent. This is because the velocity field at small scales is too weak to establish a constant kinetic energy flux as in passive scalar turbulence. A quantitative condition for the existence of the second regime is also derived in the paper.

Reynolds number effect on the velocity derivative flatness factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

On the constancy of signs and order of magnitude of Fourier–Haar coefficients

In the paper, we investigate the relation between the properties of functions and their Fourier–Haar coefficients. We show that for some classes of functions Fourier–Haar coefficients have constant signs and order of magnitude. In 1964, Golubov proved in [B. I. Golubov, On Fourier series of continuous functions with respect to a Haar system (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 28 1964, 1271–1296] that if {f(x)\in C(0,1)}, then its Fourier–Haar coefficients have constant signs when {f(x)} is a nonincreasing function on {[0,1]}, and in some cases those coefficients have a certain order of magnitude. In the present paper, we continue to investigate the properties of functions which follow from the behavior of their Fourier–Haar coefficients.

Reappraisal of the velocity derivative flatness factor in various turbulent flows

We first analytically show, starting with the Navier–Stokes equations, that the value of the derivative flatness is controlled by pressure diffusion of energy, viscous destructive effects and large-scale effects (decay and/or production). The latter two terms tend to zero when the Taylor-microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$ is sufficiently large. We argue that the pressure-diffusion term should also tend to a constant at large $Re_{\unicode[STIX]{x1D706}}$. Available data for the velocity derivative flatness, $F$, in different turbulent flows are re-examined and interpreted in the light of the finite-Reynolds-number effect. It is found that $F$ can differ from flow to flow at moderate $Re_{\unicode[STIX]{x1D706}}$; for a given flow, $F$ may also depend on the initial conditions. The data for $F$ in various flows, e.g. along the axis in the far field of plane and circular jets, and grid turbulence, show that it approaches a constant, with a value slightly larger than 10, when $Re_{\unicode[STIX]{x1D706}}$ is sufficiently large. This behaviour for $F$ is supported, at least qualitatively, by our analytical considerations. The constancy of $F$ at large $Re_{\unicode[STIX]{x1D706}}$ violates the refined similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) to account for the intermittency of the energy dissipation rate. It is not, however, inconsistent with Kolmogorov’s original similarity hypothesis (Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303), although we contend that the power-law relation $F\sim Re_{\unicode[STIX]{x1D706}}^{\unicode[STIX]{x1D6FC}_{4}}$ (Kolmogorov 1962), which is widely accepted in the literature, has in reality been almost invariably used to ‘model’ the finite-Reynolds-number effect for the laboratory data and has been strongly influenced by the weighting given to the atmospheric surface layer data. The inclusion of the latter data has misled previous investigations of how $F$ varies with $Re_{\unicode[STIX]{x1D706}}$.

Resonance tongues for the Hill equation with Duffing coefficients and instabilities in a nonlinear beam equation

We consider a class of Hill equations where the periodic coefficient is the squared solution of some Duffing equation plus a constant. We study the stability of the trivial solution of this Hill equation and we show that a criterion due to Burdina [Boundedness of solutions of a system of differential equations, Dokl. Akad. Nauk. SSSR 92 (1953) 603–606] is very helpful for this analysis. In some cases, we are also able to determine exact solutions in terms of Jacobi elliptic functions. Overall, we obtain a fairly complete picture of the stability and instability regions. These results are then used to study the stability of nonlinear modes in some beam equations.

The genus Eryma Meyer, 1840 (Crustacea: Decapoda: Erymidae): new synonyms, systematic and stratigraphic implications

Among Erymidae Van Straelen, 1925 (Van Straelen V. 1925. Contribution à l'étude des crustacés décapodes de la période jurassique. Mémoires de la Classe des Sciences de l'Académie royale de Belgique 7: 1–462), typical Mesozoic crustaceans, the genus Eryma Meyer, 1840 (Meyer H. von. 1840a. Briefliche Mittheilungen. Neues Jahrbuch für Mineralogie, Geognosie, Geologie und Petrefactenkunde 576–587) includes the largest number of species, mainly from Jurassic deposits. However, the lack of clear diagnoses for erymid genera has led to mistakes in generic assignments and to the establishment of redundant genera. The review of the concept of Eryma herein presents an attempt to clarify its diagnosis, mainly supported by the carapace groove pattern and the morphology of chelae of the first pair of pereiopods, and to emphasize its systematic implications. Thus, we maintain the synonymy of Klytia Meyer, 1840, Bolina Münster, 1839 (Münster G. 1839. Decapoda Macrura. Abbildung und Beschreibung der Fossilen Langschwänzigen Krebse in den Kalkschiefern von Bayern. Beiträge zur Petrefaktenkunde 2: 1–88) (sensu Étallon [Étallon A. 1859. Description des crustacés fossiles de la Haute-Saône et du Haut-Jura. Bulletin de la Société géologique de France 16: 169–205]), and Erymastacus Beurlen, 1928 (Beurlen K. 1928. Die Decapoden des Schwäbischen Jura mit Ausnahme der aus den oberjurassischen Plattenkalken stammenden. Palaeontographica 70: 115–278) with Eryma. Moreover, a review of the genera Protoclytiopsis Birshtein, 1958 (Birshtein JA. 1958. Ein Vertreter der ältesten Ordo der Crustacea Decapoda Protoclitiopsis antiqua gen. nov. sp. nov. aus dem Permo West-Sibiriens. Doklady Akademii Nauk, SSSR 122: 477–480), and Galicia Garassino and Krobicki, 2002 (Garassino A, Krobicki M. 2002. Galicia marianae n. gen., n. sp. (Crustacea, Decapoda, Astacidea) from the Oxfordian (Upper Jurassic) of the Southern Polish Uplands. Bulletin of the Mizunami Fossil Museum 29: 51–59), reveals the presence of a junction between the postcervical and branchiocardiac grooves. This feature is diagnostic of Eryma and supports the integration of these genera into the synonymy of Eryma. The addition of Protoclytiopsis to the synonymy of Eryma makes Eryma antiquum (Birshtein, 1958) nov. comb. the oldest representative of the genus and of the family, extending its stratigraphic range to the Late Permian (Changhsingian). Thus, this work also emphasizes that Erymidae crossed the Permian-Triassic boundary.