**292**

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**The effect of submeso motions on second-order moment budgets in the stable atmospheric boundary layer**

Schiavon, M.; Tampieri, F.; Caggio, M.; Bodnár, Tomáš

2020 - English
The effect of submeso motions on small-scale turbulence is studied considering the budget of the vertical flux of stream-wise momentum, ⟨uw⟩, in the atmospheric stable boundary layer (SBL). A parameter expressing the strength of the submeso effect is defined, and the budget is evaluated from observations both for small and large submeso effect. It results that submeso motions affect the efficiency of the vertical transport by small-scale turbulence, having implications on the terms composing the momentum flux budget and on its corresponding closures.
Keywords:
*submeso motions; pressure redistribution; second-order moment equations*
Available in digital repository of the ASCR
The effect of submeso motions on second-order moment budgets in the stable atmospheric boundary layer

The effect of submeso motions on small-scale turbulence is studied considering the budget of the vertical flux of stream-wise momentum, ⟨uw⟩, in the atmospheric stable boundary layer (SBL). A ...

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**Excessive extrapolations of Einstein's equations**

Křížek, Michal; Somer, L.

2020 - English
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.
Keywords:
*Einstein's equations; Schwarzschild solution; Friedmann equation*
Fulltext is available at external website.
Excessive extrapolations of Einstein's equations

The standard cosmological model is surprisingly quite thoroughly investigated even though it possesses many paradoxes. We present several arguments indicating why excessive extrapolations of ...

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**A critical review of paradoxes in the special theory of relativity**

Křížek, Michal

2020 - English
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.
Keywords:
*Lorentz transformation; theory of groups; inertial systems*
Fulltext is available at external website.
A critical review of paradoxes in the special theory of relativity

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 ...

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**Recent results on the problem of motion of viscous fluid around a rotating rigid body**

Deuring, P.; Kračmar, Stanislav; Nečasová, Šárka

2020 - English
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.
Keywords:
*pointwise decay; artificial boundary; error estimates*
Available in digital repository of the ASCR
Recent results on the problem of motion of viscous fluid around a rotating rigid body

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 ...

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**Cosmology on Small Scales 2020: Excessive extrapolations and selected controversies in cosmology**

Křížek, Michal; Dumin, Y. V.

2020 - English
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 dark-matter particles failed, and a number of other problems with the existence of dark energy and dark matter (such as the anomalous friction in the dark-matter 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.
Keywords:
*cosmology*
Fulltext is available at external website.
Cosmology on Small Scales 2020: Excessive extrapolations and selected controversies in cosmology

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 ...

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**Note on the problem of compressible non-Newtonian fluids**

Caggio, M.; Nečasová, Šárka

2019 - English
The aim of the paper is to consider the compressible non-Newtonian 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.
Keywords:
*non-Newtonian fluid; compressible fluid; multipolar fluid; measure-valued solution*
Available in digital repository of the ASCR
Note on the problem of compressible non-Newtonian fluids

The aim of the paper is to consider the compressible non-Newtonian fluids of power law type when the viscosity coeffcients depend not only on invariants of velocity field but also on the density. We ...

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**Programs and Algorithms of Numerical Mathematics 19 : Hejnice, June 24-29, 2018 : proceedings of seminar**

Chleboun, J.; Kůs, Pavel; Přikryl, Petr; Rozložník, Miroslav; Segeth, Karel; Šístek, Jakub; Vejchodský, Tomáš

2019 - English
These proceedings contain peer-reviewed papers that are based on the invited lectures, survey lectures, short communications, and posters presented at the 19th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in the International Center for Spiritual Rehabilitation, Hejnice, Czech Republic, June 24-29, 2018. The seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EU-MATHS-IN.cz, Czech Network for Mathematics in Industry, and with the financial support provided by the RSJ Foundation. It continued the previous seminars on mathematical software and numerical methods held (biennially, with only one exception) in Alšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, and Prague in the period 1983-2016. The objective of this series of seminars is to provide a forum for presenting and discussing advanced topics in numerical analysis, computer implementation of numerical algorithms, new approaches to mathematical modeling, and single- or multi-processor applications of computational methods.
Keywords:
*numerical mathematics*
Available in digital repository of the ASCR
Programs and Algorithms of Numerical Mathematics 19 : Hejnice, June 24-29, 2018 : proceedings of seminar

These proceedings contain peer-reviewed papers that are based on the invited lectures, survey lectures, short communications, and posters presented at the 19th seminar Programs and Algorithms of ...

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**On the mechanisms of dimensional transition in stably stratified turbulent fluid layers**

Caggio, M.; Bodnár, Tomáš; Schiavon, M.

2019 - English
The purpose of this short review communication is to present some recent results on the effects of stable density stratification on the three-dimensional 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 two-dimensional vertically stratifed flows and possible applications for stably stratifed atmospheric boundary layer will be shortly discussed.
Keywords:
*stable density stratification; kinetic and potential energy transfer; atmospheric boundary layer*
Available in digital repository of the ASCR
On the mechanisms of dimensional transition in stably stratified turbulent fluid layers

The purpose of this short review communication is to present some recent results on the effects of stable density stratification on the three-dimensional turbulent dynamics of 'thin' fluid layers ...

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**Numerical tests of far-field boundary conditions for stably stratified flows**

Bodnár, Tomáš; Fraunié, P.; Řezníček, Hynek

2019 - English
This numerical study presents the results of simulations of stably stratified wall-bounded flows. The effect of artificial far-field boundary conditions is studied in detail. The standard homogeneous Neumann condition for pressure is replaced by a non-homogeneous condition depending on local velocity and its gradient. The two-dimensional 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 far-field artifcial boundary condition. The model is based on Boussinesq approximation of non-homogeneous Navier-Stokes equations, solved using artificial compressibility method, looking for a steady solution.
Keywords:
*boussinesq approximation; stable stratification; far-field boundary condition*
Available in digital repository of the ASCR
Numerical tests of far-field boundary conditions for stably stratified flows

This numerical study presents the results of simulations of stably stratified wall-bounded flows. The effect of artificial far-field boundary conditions is studied in detail. The standard homogeneous ...

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**Multivariate smooth interpolation that employs polyharmonic functions**

Segeth, Karel

2019 - English
We study the problém of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomials therms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example is presented.
Keywords:
*data interpolation; smooth interpolation; polyharmonic spline; radial basis function*
Available in digital repository of the ASCR
Multivariate smooth interpolation that employs polyharmonic functions

We study the problém of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining ...

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