Velocity selection problem for combined motion of melting and solidification fronts

We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial melting of solid alloys. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by diffusion in the liquid film, whereas the process with only one melting front would be controlled by the very slow diffusion in the mother solid phase. The relatively weak coherency strain energy is the effective driving force for LFM. As in the classical dendritic growth problems, also in this case an exact family of steady-state solutions with two parabolic fronts and an arbitrary velocity exists if capillary effects are neglected. We develop a velocity selection theory for this problem, including anisotropic surface tension effects. The strong diffusion interaction and coherency strain effects in the solid near the melting front lead to substantial changes compared to classical dendritic growth.Comment: submitted to PR

The Issue of Harmonization of Legislation on Public Companies in the Countries of the Integration Project “New Silk Road”

Public companies in the “New Silk Road” countries are the only effective economic entity capable, in the foreseeable future to realize the modernization of transport infrastructure, energetics and create a shared socio-cultural space in the region. Despite the fact that the concept of public enterprises varies substantially across countries of the integration project «New Silk Road» there is a common approach to solving the economic challenges that the countries of the region are facing. Political will and legislative solutions in the field of harmonization of corporate law will largely determine economic realities and political success of such a promising integration project as the «New Silk Road»

Схожість насіння та біометричні показники плодів павловнії повстис¬тої Paulownia Tomentosa Steud. різного географічного походження

Paulownia tomentosa Steud. – rapid growing wood breed, capable to regenerate many times by sprout shoots after the cutting of tree and accelerating the growth of subsequent generations, it is a perspective for plantation cultivation in Ukraine. The purpose of the work is to investigate the germination quality of the seeds of the Paulownia tomentosa and the biometric indicators of the fruits and seeds, depending on the geographical origin of the trees, to evaluate the possibility of using the zoned seeds for the cultivation of high quality planting material. Biometric indicators were determined on the basis of measurements of the size of the fruits obtained in different geographical regions of Ukraine (Lviv, Transcarpathian and Odessa oblasts). To determine the effect of temperature on crop quality, germination of seeds was carried out at two temperature regimes: +15…20 °С and +21…25 °С. To determine the effect of the duration of pre-wetting on similarity indicators, seeds were soaked in water with a temperature of +20 °С 24 and 48 hours. In the conditions of the Odessa region, Paulownia tomentosa forms larger fruits, the weight of which is dominated by a mass of fruits from the Transcarpathian and Lviv regions by 24 and 38 %. Seeds of this origin are heavier and are characterized by higher sprouting rates and the friendly appearance of seed germinations. In the temperature mode of sprouting + 20…25 °С, the technical germination of the Paulownia tomentosa seeds varies from 88 to 99 %, regardless of geographical origin. At pre-soaked seeds in water for 48 hours are increasing of germination by 4–5 %, when soaked for 24 hours – by 1–3 % compared to the control (without soaking). The energy of seed germination is increased by 10–40 % and by 8–27 %. In the seeds harvested in Odessa average of seed rest is the smallest and ranges from 6.4 to 7.3 days, which indicates a very high seed germination rate. The decrease in the temperature of germination of the Paulownia tomentosa seeds leads to a decrease in all similarity indicators. The technical germination of the seeds varies in the range of 66–79 %; compared with the germination at a temperature of + 20… 25 °С decreases in the studied index is 20–23 %. Preliminary soaking of seedlings at lower temperatures also has a positive effect on seed germination. Seeds of Paulownia tomentosa are characterized by a high technical germination, regardless of geographical origin. The temperature decreasing significantly slows the seed germination process and causes a decrease in germination indexes. The increase in the duration of the pre-wetting is due to an increase in the technical germination and energy of seed germination. In general, the studied seed of three origins is characterized by high crop qualities and can be used for growing seedling material.Наведено результати дослідження біометричних показників плодів та насіння Paulownia tomentosa Steud., заготовлених із дерев, що зростають у ґрунтово-кліматичних умовах Одеської, Закарпатської та Львівської областей. Встановлено, що в умовах Одеської області павловнія повстиста формує більші плоди. Насіння цього походження характеризується значною швидкістю проростання та дружністю появи сходів. Досліджено вплив змінного температурного режиму пророщування на посівні якості насіння різного географічного походження. Встановлено, що зниження температури пророщування спричиняє зменшення енергії проростання, лабораторної та абсолютної схожості насіння, збільшує середній насінний спокій. Оцінено вплив тривалості попереднього намочування на схожість насіння. Виявлено, що попереднє намочування насіння істотно підвищує показники схожості, його тривалість пов'язується з показниками енергії проростання, технічної та абсолютної схожості. Встановлено, що серед трьох походжень насіння найвища технічна схожість характерна для насіння з Львівської області. Насіння з Одеської області має найвищу енергію проростання. Загалом досліджуване насіння всіх трьох походжень характеризується високими посівними якостями, що свідчить про можливість використання районованого насіння для вирощування садивного матеріалу і створення насаджень з притаманною для материнських рослин біологічною стійкістю, зокрема до впливу низьких температур у конкретних ґрунтово-кліматичних умовах

Simulations of three-dimensional dendritic growth using a coupled thermo-solutal phase-field model

Using a phase field model, which fully couples the thermal and solute concentration field, we present simulation results in three dimensions of the rapid dendritic solidification of a class of dilute alloys at the meso scale. The key results are the prediction of steady state tip velocity and radius at varying undercooling and thermal diffusivities. Less computationally demanding 2-dimensional results are directly compared with the corresponding 3-dimensional results, where significant quantitative differences emerge. The simulations provide quantitative predictions for the range of thermal and solutal diffusivities considered and show the effectiveness and potential of the computational techniques employed. These results thus provide benchmark 3-dimensional computations, allow direct comparison with underlying analytical theory, and pave the way for further quantitative results

Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page

Influence of external flows on crystal growth: numerical investigation

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Peclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Peclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some images had to be substantially reduced in comparison to original, resulting in low qualit

Scaling Relations of Viscous Fingers in Anisotropic Hele-Shaw Cells

Viscous fingers in a channel with surface tension anisotropy are numerically studied. Scaling relations between the tip velocity v, the tip radius and the pressure gradient are investigated for two kinds of boundary conditions of pressure, when v is sufficiently large. The power-law relations for the anisotropic viscous fingers are compared with two-dimensional dendritic growth. The exponents of the power-law relations are theoretically evaluated.Comment: 5 pages, 4 figure

The first dinosaur egg from the Lower Cretaceous of Western Siberia, Russia

© 2017 Informa UK Limited, trading as Taylor & Francis Group The Lower Cretaceous Ilek Formation in Western Siberia (Russia) has yielded various vertebrate fossils, including skeletal remains of dinosaurs. Here we report on a fragmentary theropod egg from the vertebrate locality Shestakovo 3 of the Ilek Formation in Kemerovo Province. We assign the specimen to the oogenus Prismatoolithus (oofamily Prismatoolithidae) as Prismatoolithus ilekensis oosp. nov., on the basis of the following unique combination of characters: ovoid-shaped egg; thin eggshell 300–330 μm thick; angustiprismatic morphotype; eggshell with three different layers; gradual transition between mammillary layer and prismatic layer; abrupt contact between prismatic layer and external layer; mammillary layer to prismatic layer to external layer thickness ratio is 1:3:0.6; prismatic layer with ill-defined squamatic texture; angusticanaliculate pore system; and smooth outer surface. Like other Early Creataceous Prismatoolithus, the egg of Prismatoolithus ilekensis oosp. nov. was laid by a small bodied theropod dinosaur (troodontid or primitive bird) and this taxonomic attribution is supported by results of our phylogenetic analysis. Prismatoolithus ilekensis oosp. nov. is the first Early Cretaceous ootaxon from Russia. urn:lsid:zoobank.org:act:734EAD40-86C3-488B-A61E-B5FF7378BC0

Phase-Field Approach for Faceted Solidification

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that correspond to faceted orientations. The phase-field equations are solved in the thin-interface limit with local equilibrium at the solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E53, R3017 (1996)]. The convergence of our approach is first demonstrated for equilibrium shapes. The growth of faceted needle crystals in an undercooled melt is then studied as a function of undercooling and the cusp amplitude delta for a gamma-plot of the form 1+delta(|sin(theta)|+|cos(theta)|). The phase-field results are consistent with the scaling law "Lambda inversely proportional to the square root of V" observed experimentally, where Lambda is the facet length and V is the growth rate. In addition, the variation of V and Lambda with delta is found to be reasonably well predicted by an approximate sharp-interface analytical theory that includes capillary effects and assumes circular and parabolic forms for the front and trailing rough parts of the needle crystal, respectively.Comment: 1O pages, 2 tables, 17 figure

The astrometric Gaia-FUN-SSO observation campaign of 99 942 Apophis

Astrometric observations performed by the Gaia Follow-Up Network for Solar System Objects (Gaia-FUN-SSO) play a key role in ensuring that moving objects first detected by ESA's Gaia mission remain recoverable after their discovery. An observation campaign on the potentially hazardous asteroid (99 942) Apophis was conducted during the asteroid's latest period of visibility, from 12/21/2012 to 5/2/2013, to test the coordination and evaluate the overall performance of the Gaia-FUN-SSO . The 2732 high quality astrometric observations acquired during the Gaia-FUN-SSO campaign were reduced with the Platform for Reduction of Astronomical Images Automatically (PRAIA), using the USNO CCD Astrograph Catalogue 4 (UCAC4) as a reference. The astrometric reduction process and the precision of the newly obtained measurements are discussed. We compare the residuals of astrometric observations that we obtained using this reduction process to data sets that were individually reduced by observers and accepted by the Minor Planet Center. We obtained 2103 previously unpublished astrometric positions and provide these to the scientific community. Using these data we show that our reduction of this astrometric campaign with a reliable stellar catalog substantially improves the quality of the astrometric results. We present evidence that the new data will help to reduce the orbit uncertainty of Apophis during its close approach in 2029. We show that uncertainties due to geolocations of observing stations, as well as rounding of astrometric data can introduce an unnecessary degradation in the quality of the resulting astrometric positions. Finally, we discuss the impact of our campaign reduction on the recovery process of newly discovered asteroids.Comment: Accepted for publication in A&