Relativistic calculations of charge transfer probabilities in U92+ - U91+(1s) collisions using the basis set of cubic Hermite splines

A new approach for solving the time-dependent two-center Dirac equation is presented. The method is based on using the finite basis set of cubic Hermite splines on a two-dimensional lattice. The Dirac equation is treated in rotating reference frame. The collision of U92+ (as a projectile) and U91+ (as a target) is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are calculated for different values of the impact parameter. The obtained results are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals was employed. This work can provide a new tool for investigation of quantum electrodynamics effects in heavy-ion collisions near the supercritical regime

On the meteor trail spectra

Meteor radiation appears as a result of collisions between meteoroid atoms and air molecules. Depending on duration, this radiation is usually divided into the following types: radiation of the meteor head; radiation of a coma surrounding or immediately following the meteor head; radiation of a trail formed as a result of fragments lagging behind or by the afterglow; and radiation of a meteor train forming from a tail as a result of various chemical and dynamical processes. To investigate physical processes caused by each of the above types, it is necessary to obtain the corresponding experimental data. The physical processes of the radiation and the measurement of the experimental data is discussed

Relativistic calculations of the U91+(1s)-U92+ collision using the finite basis set of cubic Hermite splines on a lattice in coordinate space

A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The relativistic calculations of the excitation and charge-transfer probabilities in the U91+(1s)-U92+ collisions in two and three dimensional approaches are performed. The obtained results are compared with our previous calculations employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated within the monopole approximation

Relativistic calculations of the K-K charge transfer and K-vacancy production probabilities in low-energy ion-atom collisions

The previously developed technique for evaluation of charge-transfer and electron-excitation processes in low-energy heavy-ion collisions [I.I. Tupitsyn et al., Phys. Rev. A 82, 042701(2010)] is extended to collisions of ions with neutral atoms. The method employs the active electron approximation, in which only the active electron participates in the charge transfer and excitation processes while the passive electrons provide the screening DFT potential. The time-dependent Dirac wave function of the active electron is represented as a linear combination of atomic-like Dirac-Fock-Sturm orbitals, localized at the ions (atoms). The screening DFT potential is calculated using the overlapping densities of each ions (atoms), derived from the atomic orbitals of the passive electrons. The atomic orbitals are generated by solving numerically the one-center Dirac-Fock and Dirac-Fock-Sturm equations by means of a finite-difference approach with the potential taken as the sum of the exact reference ion (atom) Dirac-Fock potential and of the Coulomb potential from the other ion within the monopole approximation. The method developed is used to calculate the K-K charge transfer and K-vacancy production probabilties for the Ne$(1s^2 2s^2 2p^6)$ -- F$^{8+}(1s)$ collisions at the F$^{8+}(1s)$ projectile energies 130 keV/u and 230 keV/u. The obtained results are compared with experimental data and other theoretical calculations. The K-K charge transfer and K-vacancy production probabilities are also calculated for the Xe -- Xe$^{53+}(1s)$ collision.Comment: 16 pages, 4 figure

Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type

We consider the special type of the field-theoretical Symplectic structures called weakly nonlocal. The structures of this type are in particular very common for the integrable systems like KdV or NLS. We introduce here the special class of the weakly nonlocal Symplectic structures which we call the weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of "averaging" of the weakly nonlocal Symplectic structures. The averaging procedure gives the weakly nonlocal Symplectic Structure of Hydrodynamic Type for the corresponding Whitham system. The procedure gives also the "action variables" corresponding to the wave numbers of $m$-phase solutions of initial system which give the additional conservation laws for the Whitham system.Comment: 64 pages, Late

Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas

We consider Novikov problem of the classification of level curves of quasiperiodic functions on the plane and its connection with the conductivity of two-dimensional electron gas in the presence of both orthogonal magnetic field and the superlattice potentials of special type. We show that the modulation techniques used in the recent papers on the 2D heterostructures permit to obtain the general quasiperiodic potentials for 2D electron gas and consider the asymptotic limit of conductivity when $\tau \to \infty$. Using the theory of quasiperiodic functions we introduce here the topological characteristics of such potentials observable in the conductivity. The corresponding characteristics are the direct analog of the "topological numbers" introduced previously in the conductivity of normal metals.Comment: Revtex, 16 pages, 12 figure

Утилизация сульфидно-мышьяковистого кека

When processing sulfide copper-zinc concentrates at copper smelters, sulfide-arsenic cakes are formed, which are subject to disposal. To solve the global environmental problem of arsenic in the metallurgical and mining industries, it must be reliably concentrated and fixed in technological flows with subsequent waste disposal. The fusion of arsenic cake with elemental sulfur leads to the formation of vitreous sulfides, which are less toxic in comparison with dispersed powdered cake, homogeneous and compact in shape. The fusion product is represented by non-stoichiometric arsenic sulfide, similar in composition to As2S5. The high chemical stability of glassy arsenic sulfides is confirmed by the results of leaching by TCLP method. The fusion products have 100 times lower solubility compared to the initial cake. Achieving the solubility of arsenic in the alloy below the threshold concentration (5 mg/dm3 ) makes it possible to recommend the disposal of arsenic cake by fusing it with elemental sulfur. The fusion products belong to non-hazardous waste and are suitable for long-term storage. The composition and structure of cake fusions with iron powder have been studied. New compounds of variable composition were identified in the fused samples: arsenides and sulfides of iron, arsenic sulfides and arsenopyrites. Studies have shown that the products of fusion with iron have a solubility 10–15 times lower than the arsenic compounds in the initial cake but above the threshold concentration as per TCLP method. Therefore, fusion with iron cannot be recommended for practical use for the disposal of arsenic cakes.При переработке сульфидных медно-цинковых концентратов на медеплавильных заводах образуются сульфидномышьяковистые кеки, подлежащие утилизации. Для решения глобальной экологической проблемы мышьяка в металлургической и горнодобывающей отраслях промышленности он должен быть надежно сконцентрирован и иммобилизован в технологических потоках с последующим удалением отходов. Сплавление мышьяковистого кека с элементной серой приводит к образованию стекловидных сульфидов, которые менее токсичны в сравнении с дисперсным порошкообразным кеком, однородны и обладают компактной формой. Продукт сплавления представлен нестехиометрическим сульфидом мышьяка, близким по составу к As2S5. Высокая химическая устойчивость стеклообразных сульфидов мышьяка подтверждается результатами выщелачивания по методике TCLP. Продукты сплавления имеют в 100 раз меньшую растворимость по сравнению с исходным кеком. Достижение растворимости мышьяка в сплаве ниже пороговой концентрации (5 мг/дм3 ) позволяет рекомендовать утилизацию мышьяковистого кека способом сплавления его с элементной серой. Продукты сплавления относятся к неопасным отходам и пригодны для длительного хранения. Изучены состав и структура сплавов кека с железным порошком. В сплавленных образцах выявлены новые соединения переменного состава: арсениды и сульфиды железа, сульфиды мышьяка и арсенопириты. Исследования показали, что продукты сплавления с железом обладают растворимостью в 10–15 раз меньшей, чем соединения мышьяка в исходном кеке, но выше пороговой концентрации по методике TCLP. Поэтому сплавление с железом не может быть рекомендовано к практическому использованию для утилизации мышьяковистых кеков

Scalable stellar evolution forecasting: Deep learning emulation vs. hierarchical nearest neighbor interpolation

Many astrophysical applications require efficient yet reliable forecasts of stellar evolution tracks. One example is population synthesis, which generates forward predictions of models for comparison with observations. The majority of state-of-the-art population synthesis methods are based on analytic fitting formulae to stellar evolution tracks that are computationally cheap to sample statistically over a continuous parameter range. Running detailed stellar evolution codes, such as MESA, over wide and densely sampled parameter grids is prohibitively expensive computationally, while stellar-age based linear interpolation in-between sparsely sampled grid points leads to intolerably large systematic prediction errors. In this work, we provide two solutions of automated interpolation methods that find satisfactory trade-off points between cost-efficiency and accuracy. We construct a timescale-adapted evolutionary coordinate and use it in a two-step interpolation scheme that traces the evolution of stars from zero age main sequence all the way to the end of core helium burning while covering a mass range from ${0.65}$ to $300 \, \mathrm{M_\odot}$. The feedforward neural network regression model (first solution) that we train to predict stellar surface variables can make millions of predictions, sufficiently accurate over the entire parameter space, within tens of seconds on a 4-core CPU. The hierarchical nearest neighbor interpolation algorithm (second solution) that we hard-code to the same end achieves even higher predictive accuracy, the same algorithm remains applicable to all stellar variables evolved over time, but it is two orders of magnitude slower. Our methodological framework is demonstrated to work on the MIST data set. Finally, we discuss prospective applications and provide guidelines how to generalize our methods to higher dimensional parameter spaces.Comment: Submitted to A&