**371**

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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*
Available in digital repository of the ASCR
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*
Available in digital repository of the ASCR
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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**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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**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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**Analysis of the turbulence parameterisations for the atmospheric surface layer**

Caggio, Matteo; Bodnár, Tomáš

2018 - English
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer in function of the stability of the atmosphere. The case of very stable conditions (strong strati cation), where theoretical approaches provide conflicting results (see Luhar et al. [11]), is analysed in detail to provide some insight into the limits of applicability for some of the most popular models of turbulence. The problem of the existence of the critical flux Richardson number is also taken into account.
Keywords:
*atmospheric boundary layer; Monin-Obukhov similarity theory; turbulence parameterisations; strong strati cation*
Available in digital repository of the ASCR
Analysis of the turbulence parameterisations for the atmospheric surface layer

The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer in function of the stability of the atmosphere. The case of ...

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**Classification of distances in cosmology**

Křížek, Michal; Mészáros, A.

2018 - English
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single natural distance, since the universe is expanding, curved, and we look back in time. In this survey paper we will concentrate on geometrical interpretations of the above-mentioned distances.
Keywords:
*standard cosmological model; cosmological principle; Friedmann equation; cosmological parameters; Einstein static universe*
Available in digital repository of the ASCR
Classification of distances in cosmology

In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single ...

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**Parallel domain decomposition solver for flows in hydrostatic bearings**

Hanek, Martin; Šístek, Jakub; Burda, P.; Stach, E.

2018 - English
We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used for discretization. The arising nonlinear system of algebraic equations is linearized using the Picard’s iteration, and the Balancing Domain Decomposition based on Constraints (BDDC) method is used to solve the linear systems of equations. The solver is first validated with an experiment for the case of a bearing without motion, and it is then applied to simulation of flow in a sliding bearing.
Keywords:
*hydrostatic bearings; BDDC*
Available in digital repository of the ASCR
Parallel domain decomposition solver for flows in hydrostatic bearings

We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used ...

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**Neglected gravitational redshift in detections of gravitational waves**

Křížek, Michal; Somer, L.

2018 - English
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the authors have not taken into account a large gravitational redshift of this binary system, which is a direct consequence of time dilation in a strong gravitational field. Thus the proposed masses are overestimated. In our paper we also give other arguments for this statement.
Keywords:
*gravitational redshift; time dilatation; black holes; wavelets*
Available in digital repository of the ASCR
Neglected gravitational redshift in detections of gravitational waves

In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the ...

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