Temperature field around a spherical, cylindrical, and needle-shaped crystal, growing in a pre-cooled melt

The growth of a single crystal in a precooled melt was examined. The conditions under which this occurs are described. It is found that the movement of the crystallization front is proportional to the root of time. The problem is solved based on the presented considerations

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»

Quantitative phase-field modeling of solidification at high Lewis number

A phase-field model of nonisothermal solidification in dilute binary alloys is used to study the variation of growth velocity, dendrite tip radius, and radius selection parameter as a function of Lewis number at fixed undercooling. By the application of advanced numerical techniques, we have been able to extend the analysis to Lewis numbers of order 10 000, which are realistic for metals. A large variation in the radius selection parameter is found as the Lewis number is increased from 1 to 10 000

Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion

Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these nonlinear processes are governed by an infinite number of conservation laws. Moreover, in many cases {\it all dynamics of the interface can be reduced to the linear time--dependence of only one ``moment" $M_0$} which corresponds to the changing volume while {\it all higher moments, $M_l$, are constant in time. These moments have a purely geometrical nature}, and thus carry information about the moving shape. These conserved quantities (eqs.~(7) and (8) of this article) are interpreted as coefficients of the multipole expansion of the Newtonian potential created by the mass uniformly occupying the domain enclosing the moving interface. Thus the question of how to recover the moving shape using these conserved quantities is reduced to the classical inverse potential problem of reconstructing the shape of a body from its exterior gravitational potential. Our results also suggest the possibility of controlling a moving interface by appropriate varying the location and strength of sources and sinks.Comment: CYCLER Paper 93feb00

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

Convective and Conductive Selection Criteria of a Stable Dendritic Growth and Their Stitching

The paper deals with the analysis of stable thermo-solutal dendritic growth in the presence of intense convection. The n-fold symmetry of crystalline anisotropy as well as the two- and three-dimensional growth geometries are considered. The steady-state analytical solutions are found with allowance for the convective-type heat and mass exchange boundary conditions at the dendritic surface. A linear morphological stability analysis determining the marginal wavenumber is carried out. The new stability criterion is derived from the solvability theory and stability analysis. This selection criterion takes place in the regions of small undercooling. To describe a broader undercooling diapason, the obtained selection criterion, which describes the case of intense convection, is stitched together with the previously known selection criterion for the conductive-type boundary conditions. It is demonstrated that the stitched selection criterion well describes a broad diapason of experimental undercoolings. © 2020 John Wiley & Sons, Ltd.The present work comprises different parts of research studies including (i) the model formulation, stability and solvability analyses, derivation of the selection criterion in the case of intense convection, its sewing with the criterion for the conductive boundary conditions, (ii) numerical simulations, (iii) experiments, and their comparison. Different parts of the present work were supported by different grants and programs. With this in mind, the authors are grateful to the following foundations, programs, and grants. Theoretical part (i) was supported by the Russian Foundation for Basic Research (grant no. 19-32-51009). Numerical part (ii) was made possible due to the financial support of the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center, project no. 075-02-2020-1537/1). The experimental part (iii) was supported by the German Space Center Space Management under contract number 50WM1941

On the role of confinement on solidification in pure materials and binary alloys

We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.Comment: 13 pages, 9 figures, 3 table

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

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