20210328 00:00 
On the influence of diffusion stabilization in OldroydB fluid flow simulations
Pires, M. ; Bodnár, Tomáš
This work presents some numerical tests of finite element solution of incompressible OldroydB fluid flows. The effect of numerical stabilization using artificial stress diffusion is investigated in detail. The limits of Weissenberg number We for which it is possible to obtain the numerical solution were studied depending on the Reynolds number Re and the diffusion parameter. Series of numerical tests were performed for steady twodimensional OldroydB fluid flow in corrugated channel (tube). The numerical results clearly proved the advantage (higher attainable We) of stabilized numerical method over the classical formulation without the artificial stress diffusion.
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20210224 00:44 
Cosmology on Small Scales 2020: Excessive extrapolations and selected controversies in cosmology
Křížek, Michal ; Dumin, Y. V.
According to the modern cosmological paradigm, about 2/3 of the energy of the Universe is in dark form and about 5/6 of the matter is invisible. However, numerous recent independent attempts to detect darkmatter particles failed, and a number of other problems with the existence of dark energy and dark matter (such as the anomalous friction in the darkmatter halos of galaxies) become now more and more obvious. All these problems raise the question if the 'dark' substance is merely a result of the use of erroneous assumptions or incorrect models based e.g. on excessive extrapolations. Consequently, it is timely to gather specialists from various branches of astronomy and astrophysics to discuss these questions.
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20210224 00:43 
Recent results on the problem of motion of viscous fluid around a rotating rigid body
Deuring, P. ; Kračmar, Stanislav ; Nečasová, Šárka
We consider the linearized incompressible flow around rotating and translating body in the exterior domain R³D‾, where D⊂R³ is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure. Further, we consider the linearized problem in a truncation domain DR:=BRD‾ of the exterior domain R³D‾ under certain artificial boundary conditions on the truncating boundary ∂BR, and then compare this solution with the solution in the exterior domain R³D‾ to get the truncation error estimate.
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20210224 00:43 
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20201203 22:56 
A critical review of paradoxes in the special theory of relativity
Křížek, Michal
We show that the Doppler effect and aberration of light can produce more dominant and entirely opposite effects for relativistic speeds than those predicted by the Special Theory of Relativity, in particular, the clock paradox, time dilatation, and length contraction. For instance, an observer will measure a higher frequency of an approaching clock than the same clock has at rest. We also prove that under certain conditions an approaching bar on a photo may seem to have a larger length for a relativistic speed than at rest.
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20201203 22:56 
Excessive extrapolations of Einstein's equations
Křížek, Michal ; Somer, L.
The standard cosmological model is surprisingly quite thoroughly investigated even though it possesses many paradoxes. We present several arguments indicating why excessive extrapolations of Einstein's equations to cosmological distances are questionable. First, we show how to express explicitly the first of Einstein's 10 partial differential equations to demonstrate their extremely large complexity. Therefore, it would be very difficult to find their solution for two or more bodies to model, e.g., the evolution of the Solar system. Further, we present some unexpected failures of the Schwarzschild and Friedmann solution of these equations. Then we explain why application of Einstein's equations to the whole universe represents incorrect extrapolations that lead to dark matter, dark energy, and several unrealistic situations. Finally, we give 10 further arguments showing why celebrated Einstein's equations do not describe reality well.
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20191019 16:35 
Numerical tests of farfield boundary conditions for stably stratified flows
Bodnár, Tomáš ; Fraunié, P. ; Řezníček, Hynek
This numerical study presents the results of simulations of stably stratified wallbounded flows. The effect of artificial farfield boundary conditions is studied in detail. The standard homogeneous Neumann condition for pressure is replaced by a nonhomogeneous condition depending on local velocity and its gradient. The twodimensional tests are performed for the case of flow over a low isolated hill. The simulations on computational domains with three different heights are discussed to evaluate the performance of the new farfield artifcial boundary condition. The model is based on Boussinesq approximation of nonhomogeneous NavierStokes equations, solved using artificial compressibility method, looking for a steady solution.
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20191019 16:35 
Note on the problem of compressible nonNewtonian fluids
Caggio, M. ; Nečasová, Šárka
The aim of the paper is to consider the compressible nonNewtonian fluids of power law type when the viscosity coeffcients depend not only on invariants of velocity field but also on the density. We introduce approximation scheme using model of multipolar fluids. After then passing with higher viscosity to zero we get the measure valued solution of the problem.
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20191019 16:35 
On the mechanisms of dimensional transition in stably stratified turbulent fluid layers
Caggio, M. ; Bodnár, Tomáš ; Schiavon, M.
The purpose of this short review communication is to present some recent results on the effects of stable density stratification on the threedimensional turbulent dynamics of 'thin' fluid layers forced at intermediate scales. In particular, how the strati cation and the confinement affect the mechanism of kinetic and potential energy transfer between different scales. Results on twodimensional vertically stratifed flows and possible applications for stably stratifed atmospheric boundary layer will be shortly discussed.
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20190725 09:14 
Talk about patterns in the mathematics classroom
Roubíček, Filip
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical patterns in a triangle grid and their transformation into arithmetic patterns or algebraic functions. It shows how pupils/students reason about relationships in these patterns and among these patterns, how they describe and express their generalizations in words or symbols.
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