Penetrators (penetrating sondes) and new possibilities for study of the planets

The fields of possible use of penetrators in space research are considered. A survey of the condition of development and plans for use of penetrators abroad is presented and an analysis is given of the significance of scientific problems when probing planets

The oxygen isotope effect on critical temperature in superconducting copper oxides

The isotope effect provided a crucial key to the development of the BCS (Bardeen-Cooper-Schrieffer) microscopic theory of superconductivity for conventional superconductors. In superconducting cooper oxides (cuprates) showing an unconventional type of superconductivity, the oxygen isotope effect is very peculiar: the exponential coefficient strongly depends on doping level. No consensus has been reached so far on the origin of the isotope effect in the cuprates. Here we show that the oxygen isotope effect in cuprates is in agreement with the bisoliton theory of superconductivity.Comment: 3 pages including 4 figures; version 2 is with minor correction

Y2O3:Eu and the Mössbauer isomer shift coefficient of Eu compounds from ab-initio simulations

We report on a full potential density functional theory characterization of Y2O3 upon Eu doping on the two inequivalent crystallographic sites 24d and 8b. We analyze local structural relaxation, electronic properties and the relative stability of the two sites. The simulations are used to extract the contact charge density at the Eu nucleus. Then we construct the experimental isomer shift (IS) versus contact charge density calibration curve, by considering an ample set of Eu compounds: EuF3, EuO, EuF2, EuS, EuSe, EuTe, EuPd3 and the Eu metal. The, expected, linear dependence has a slope of α = 0.054 mm s-1 Å-3, which corresponds to nuclear expansion parameter ΔR/R = 6.0 × 10-5. α allows to obtain an unbiased and accurate estimation of the IS for any Eu compound. We test this approach on two mixed-valence compounds Eu3S4 and Eu2SiN3, and use it to predict the Y2O3:Eu IS with the result +1.04 mm s-1 at the 24d site and +1.00 mm s-1 at the 8b site

Y₂O₃:Eu and the Mössbauer isomer shift coefficient of Eu compounds from ab-initio simulations

We report on a full potential density functional theory characterization of Y2O3 upon Eu doping on the two inequivalent crystallographic sites 24d and 8b. We analyze local structural relaxation, electronic properties and the relative stability of the two sites. The simulations are used to extract the contact charge density at the Eu nucleus. Then we construct the experimental isomer shift (IS) versus contact charge density calibration curve, by considering an ample set of Eu compounds: EuF3, EuO, EuF2, EuS, EuSe, EuTe, EuPd3 and the Eu metal. The, expected, linear dependence has a slope of α = 0.054 mm s−1 Å−3, which corresponds to nuclear expansion parameter ΔR/R = 6.0 × 10−5. α allows to obtain an unbiased and accurate estimation of the IS for any Eu compound. We test this approach on two mixed-valence compounds Eu3S4 and Eu2SiN3, and use it to predict the Y2O3:Eu IS with the result +1.04 mm s−1 at the 24d site and +1.00 mm s−1 at the 8b site

Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

Aspicilia stalagmitica (Megasporaceae) - A new lichen species with isidia-like thalline outgrowths

Aspicilia stalagmitica Paukov et Davydov from the Altai Mts, a species with isidia-like outgrowths on areoles, is described as new to science. From other species of the genus Aspicilia stalagmitica differs by the following set of characters: short narrow marginal lobes, conidiomata in the isidia-like outgrowths, appressed to almost substipitate apothecia, long picnoconidia, and stictic acid as a main secondary metabolite. A phylogenetic analysis of Aspicilia stalagmitica (ITS) showing its relationships within Aspicilia is presented. © 2020 Altai State University. All rights reserved.Russian Foundation for Basic Research, RFBR: 18-04-00414Ministry of Education and Science of the Russian Federation, MinobrnaukaUppsala UniversitetEvgeny Davydov thanks Dr Wen-Li Chen for organizing the expedition to China. Alexander Paukov would like to thank RFBR (project 18-04-00414) and the Ministry of Education and Science of the Russian Federation (agreement no. 02.A03.21.0006) for financial support. We are grateful to Anders Nordin (Museum of Evolution, Uppsala University) whose comments have greatly improved the manuscript

Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and Astrophysic

A finite element method for fully nonlinear elliptic problems

We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretisation method is that a recovered (finite element) Hessian is a biproduct of the solution process. We build on the linear basis and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems including the Monge-Amp\`ere equation and Pucci's equation.Comment: 22 pages, 31 figure

Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates

In many molecular systems one encounters the situation where electronic excitations couple to a quasi-continuum of phonon modes. That continuum may be highly structured e.g. due to some weakly damped high frequency modes. To handle such a situation, an approach combining the non-Markovian quantum state diffusion (NMQSD) description of open quantum systems with an efficient but abstract approximation was recently applied to calculate energy transfer and absorption spectra of molecular aggregates [Roden, Eisfeld, Wolff, Strunz, PRL 103 (2009) 058301]. To explore the validity of the used approximation for such complicated systems, in the present work we compare the calculated (approximative) absorption spectra with exact results. These are obtained from the method of pseudomodes, which we show to be capable of determining the exact spectra for small aggregates and a few pseudomodes. It turns out that in the cases considered, the results of the two approaches mostly agree quite well. The advantages and disadvantages of the two approaches are discussed