Numerical Algorithms For Analysis Of Dynamics Of Ideal Fluid With Free/moving Boundaries

This thesis proposes and examines various algorithms for analysis of steady ideal fluid capillary flows with free/moving boundary.;For this class of problems, the leading parameter is the capillary number C which for an established flow and fixed geometry of the solution domain is proportional to the ratio of a velocity scale and surface tension. When C {dollar}\ll{dollar} 1 the problem can be simplified and is solved using Small Deformation Theory (SDT). Conditions for validity of SDT are identified.;When C = 0(1) one has to seek a simultaneous solution for two dependent variables, i.e. a flow field and a free surface shape. Depending on the order of linearization of the governing equations one arrives at the Picard Algorithm (linearization of the first order) and the 1-Step Algorithm (of the second order). The latter one provides significantly faster convergence.;All algorithms are based on a finite-difference approximation and the Alternate Direction Implicite (ADI) scheme has been chosen as a method of solution. A thorough study of an algebraic stability of equations of the flow field and the free surface, has been carried out. This is supplemented by an analytical and numerical analysis of existence and uniqueness of the solutions to the free surface equation. The Wachspress optimization of relaxation parameters has been used in order to accelerate convergence of the ADI.;Finite differences discretization implemented in the thesis is based on the Hermitian equations, which generated compact difference schemes of the second and higher order accuracy. In the thesis one can find a rigorous study of the interrelationship between the order of differencing scheme and the rate of convergence of the computed results with grid refining. This rate, called \u27grid-convergence order\u27 has been used as the criterion for identification of the minimum dimensionality of the computational grid. It was found that higher order methods require much finer grids than second order methods, to provide desired grid-convergence order.;For higher order method, the new fourth order compact difference estimate (independent of coordinate direction) of a mixed derivative was found. Its application significantly improved the grid-convergence order.;The discussion of the algorithms is supplemented by a physical interpretation of the results obtained for a number of particular cases

Invariant means on Abelian groups capture complementability of Banach spaces in their second duals

Let $X$ be a Banach space. Then $X$ is complemented in the bidual $X^{**}$ if and only if there exists an invariant mean $\ell_\infty(G, X)\to X$ with respect to a free Abelian group $G$ of rank equal to the cardinality of $X^{**}$, and this happens if and only if there exists an invariant mean with respect to the additive group of $X^{**}$. This improves upon previous results due to Bustos Domecq =and the second-named author, where certain idempotent semigroups of cardinality equal to the cardinality of $X^{**}$ were considered, and answers a question of J.M.F. Castillo (private communication). En route to the proof of the main result, we endow the family of all finite-dimensional subspaces of an infinite-dimensional vector space with a structure of a free commutative monoid with the property that the product of two subspaces contains the respective subspaces, which is possibly of interest in itself.Comment: 12 pp., accepted for publication in Studia Mathematic

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wywiad z: Trojańczyk, Ada

Mapping Natura 2000 Habitat Conservation Status in a Pannonic Salt Steppe with Airborne Laser Scanning

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Biodiversity mapping via Natura 2000 conservation status and ebv assessment using airborne laser scanning in alkali grasslands

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UB-studio’s reserveren via Planon

De Universiteitsbibliotheek stelt voor haar studenten en medewerkers ruimtes beschikbaar voor studie en overleg. Reservering van een studiec.q. overlegruimte voltrok zich tot voor kort in een Excelsheet. Pictogram sprak met Adam Kania over de overgang naar een reserveringsysteem

Joseph the MoUSE : Mouse Ultrasonic Sound Explorer

Joseph the MoUSE — Mouse Ultrasonic Sound Explorer (MoUSE) software aims to address the issue of manual analysis of recordings from experiments on rodents by introducing automatic techniques for ultrasonic vocalization (USV) detection. It combines deep learning (DL) methods with classical pattern recognition and computer graphics algorithms. During development, we used a dataset that consisted of recordings from real-world experiments in the open field. Recordings like these pose obstacles to automatic USV detection, one of which is the noise produced by mice in the experimental area or in nearby cages. Therefore, additionally, we conducted research and implemented de-noising methods along with detection algorithms. The project includes Python packages with algorithms for sound noise removal and USV detection, and provides a user-friendly graphical interface