Mathematical modelling of process of salt transfer under filtration and moisture transfer in saturated and non-saturated soil mass with available mobile free surface

Здійснено математичне моделювання процесу солепереносу при сумісній фільтрації підземних вод та вологопереносі в насичено-ненасиченому ґрунтовому середовищі. Розглянуто задачу безнапірної стаціонарної фільтрації сольових розчинів за наявності рухомої вільної поверхні ґрунтових вод, яка задана на межі областей повного та неповного насичення. Вважається, що сольові розчини находять у ґрунтове середовище з поверхні області неповного насичення і вимиваються через дрену (осушувальний режим). На основі побудованої математичної моделі даної крайової задачі проведено дослідження процесу солепереносу до дрени в області повного насичення та процесу вологопереносу з урахуванням солепереносу в області неповного насичення ґрунту; досліджено протікання даних процесів сумісно для обох областей водонасичення. Чисельні розв’язки відповідних крайових задач знайдено методом скінченних різниць із використанням чисельних конформних відображень. На основі програмної реалізації задачі проведено чисельні експерименти та здійснено їх аналіз.The mathematical modelling of the process of salt transfer under joint filtration of ground waters and moisture transfer in saturated-non-saturated soil medium has been carried out. The problem of the free flow stationary filtration of salt solutions under the available mobile free surface of ground waters which is set at the boundary of areas of complete and incomplete saturation has been considered. It is believed that salt solutions enter soil medium from the surface of incomplete saturation and are washed out via drain, i.e. the problem of salt transfer is considered in the case of drainage regime. On the basis of the built mathematical model of this boundary problem the research of the process of salt transfer to the drain in the area of complete saturation and of the process of moisture transfer taking into account salt transfer in the area of incomplete soil saturation has been conducted. The comprehensive study of the process of salt transfer in areas of complete and incomplete saturation is carried out. For this purpose these areas of water saturation are considered as one entity with common unknown boundary which is in the process of problem solution. It makes possible to find the interconnection between investigated processes and to carry out their prediction in the area of saturated-non-saturated soil medium. On the basis of the comprehensive solution of the problem the change of free surface under the influence of processes studied has been established. Numerical solutions of relevant boundary problems are determined by the method of finite differences using numerical conformal mapping. On the basis of programmed implementation of the problem the construction of the conformal mapping in areas of filtration flow, moisture flow and conformal differential network of the area of saturated-non-saturated soil medium has been done; there have been received numerical results and graphical representation of the distribution of the field of piezometric pressure heads, of moisture pressure heads and of concentration of salts in areas of complete and incomplete saturation and also of the distribution of the field of salt solutions concentration in saturated-non-saturated soil mass. A number of numerical experiments has been conducted which gave the possibility to carry out the analysis of results obtained with different initial data of the problem and to research in detail the nature of the action of the process of salt transfer under filtration and of moisture transfer in saturated-non-saturated soil medium

Magnetic field structure in single late-type giants: Beta Ceti in 2010 - 2012

The data were obtained using two spectropolarimeters - Narval at the Bernard Lyot Telescope, Pic du Midi, France, and ESPaDOnS at CFHT, Hawaii. Thirty-eight circularly-polarized spectra have been collected in the period June 2010 - January 2012. The Least Square Deconvolution method was applied for extracting high signal-to-noise ratio line profiles, from which we measure the surface-averaged longitudinal magnetic field Bl. Chromospheric activity indicators CaII K, H_alpha, CaII IR (854.2 nm) and radial velocity were simultaneously measured and their variability was analysed together with the behavior of Bl. The Zeeman Doppler Imaging (ZDI) inversion technique was employed for reconstruction of the large-scale magnetic field and two magnetic maps of Beta Ceti are presented for two periods (June 2010 - December 2010 and June 2011 - January 2012). Bl remains of positive polarity for the whole observational period. The behavior of the line activity indicators is in good agreement with the Bl variations. The two ZDI maps show a mainly axisymmetric and poloidal magnetic topology and a simple surface magnetic field configuration dominated by a dipole. Little evolution is observed between the two maps, in spite of a 1 yr interval between both subsets. We also use state-of-the-art stellar evolution models to constrain the evolutionary status of Beta Ceti. We derive a mass of 3.5 M_sun and propose that this star is already in the central-helium burning phase. Taking into account all our results and the evolutionary status of the star, we suggest that dynamo action alone may not be eficient enough to account for the high magnetic activity of Beta Ceti. As an alternate option, we propose that it may be an Ap star descendant presently undergoing central helium-burning and still exhibiting a remnant of the Ap star magnetic field.Comment: 10 pages; 5 figures; 3 table

Magnetic fields in single late-type giants in the Solar vicinity: How common is magnetic activity on the giant branches?

We present our first results on a new sample containing all single G,K and M giants down to V = 4 mag in the Solar vicinity, suitable for spectropolarimetric (Stokes V) observations with Narval at TBL, France. For detection and measurement of the magnetic field (MF), the Least Squares Deconvolution (LSD) method was applied (Donati et al. 1997) that in the present case enables detection of large-scale MFs even weaker than the solar one (the typical precision of our longitudinal MF measurements is 0.1-0.2 G). The evolutionary status of the stars is determined on the basis of the evolutionary models with rotation (Lagarde et al. 2012; Charbonnel et al., in prep.) and fundamental parameters given by Massarotti et al. (1998). The stars appear to be in the mass range 1-4 M_sun, situated at different evolutionary stages after the Main Sequence (MS), up to the Asymptotic Giant Branch (AGB). The sample contains 45 stars. Up to now, 29 stars are observed (that is about 64 % of the sample), each observed at least twice. For 2 stars in the Hertzsprung gap, one is definitely Zeeman detected. Only 5 G and K giants, situated mainly at the base of the Red Giant Branch (RGB) and in the He-burning phase are detected. Surprisingly, a lot of stars ascending towards the RGB tip and in early AGB phase are detected (8 of 13 observed stars). For all Zeeman detected stars v sin i is redetermined and appears in the interval 2-3 km/s, but few giants with MF possess larger v sin i.Comment: 4 pages, 3 figures, Proceedings IAU Symposium No. 302, 201