
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.


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.


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.


Survey of the basic cosmological discoveries from years 19101930
Liška, Andrej ; Mészáros, Attila (advisor) ; Křížek, Michal (referee)
Between 1910 and 1930 a large number of astronomical discoveries took place. Henrietta Swan Leavitt revealed the relationship between the luminosity and the period of Cepheids, which then bacame the indicators for distance de termination in the universe. Based on this relation in 1925 Edwin Powell Hubble calculated the distance to our neighboring Galaxy M31. Tireless exploration of the nebulae by Vesto Melvin Slipher brought a very important ratio between the red and blue shifts, where the red ones clearly dominated. In 1927 Georges Edouard Lemaître derived Hubble's law from Einstein's field equations, indepen dently on Alexander Alexandrovich Friedmann. Two years later Hubble definitely demonstrated the linear behavior between the red shift and the distance. 1


Cosmology on Small Scales 2018: Dark Matter Problem and Selected Controversies in Cosmology
Křížek, Michal ; Dumin, Y. V.
According to the standard cosmological model, our Universe needs a significant amount of dark matter, about six times more than that of the usual baryonic matter, besides an even larger amount of dark energy. But to date, both dark matter and dark energy have remained conceptually elusive, without concrete evidence based on direct physical measurements. Yet another subtle issue is that the Friedmann equation – the cornerstone of modern cosmology – was derived from the system of ten Einstein’s equations applied to a perfectly symmetric universe, which is homogeneous\nand isotropic for every fixed time instant. So, the question is whether one can perform such excessive extrapolations and, in particular, at which scale the effect of Hubble expansion is manifested.


Neglected gravitational redshift in detections of gravitational waves
Křížek, Michal ; Somer, L.
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.


Classification of distances in cosmology
Křížek, Michal ; Mészáros, A.
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, lightyear, 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 abovementioned distances.


Trends in the field management of the education in dissertations of department
Křížek, Michal ; Trojan, Václav (advisor) ; Šafránková, Jana Marie (referee)
The Management of the education is the five years old filed of study of the Faculty of Education of Charles University in Prague. This dissertation is looks for some trends of this field, based on all dissertations of the department for the period 20122016. The dissertation also provides an overview that is good for understanding of important concepts such as management, school management, educational policy or management ef education. The main goal of this dissertation is to map the development of topics and contents that have appeared during the last five years in the dissertation of the department, to analyze the problems that were most often encountered and to find out which factors influenced the selection of themes and the whole process.


Cosmological constant
Bjelka, Jakub ; Mészáros, Attila (advisor) ; Křížek, Michal (referee)
The aim of this work is concentration of the relevant knowledges from area history of the cosmological constant. Theory listed in time sequence show its origin, evolution and problems associated with it. In this work are commented static models which are made possible by the existence of a cosmological constant. Parameters obtained from experiments BAO (baryon acoustic oscillations) from Supernova Type Ia measurements (SNe) and from measurements of the cosmic microwave background (CMB) are, as the marginal conditions determined also. Furthermore, there are commented alternative solutions of the problem of cosmological constant in the form of a cyclic model or time variable of the cosmological "constant". In conclusion, there is mentioned the possibility of alternative to cosmological constant in the form of quintescence.


Fluidstructure interaction of compressible flow
Hasnedlová, Jaroslava ; Feistauer, Miloslav (advisor) ; Křížek, Michal (referee) ; Kozel, Karel (referee) ; Rannacher, Rolf (referee)
Title: Fluidstructure interaction of compressible flow Author: RNDr. Jaroslava Hasnedlová Department: Department of Numerical Mathematics, Institute of Applied Mathematics Supervisors: Prof. RNDr. Miloslav Feistauer, DrSc., Dr. h. c., Prof. Dr. Dr. h. c. Rolf Rannacher Supervisors' email addresses: feist@karlin.mff.cuni.cz, rannacher@iwr.uniheidelberg.de Abstract: The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the spacetime discretization of a nonstationary convectiondiffusion initialboundary value problem with nonlinear convection and linear diffusion. The DGFE method is applied sep arately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. The main result is the proof of error estimates in L2 (L2 )norm and in DGnorm formed by the L2 (H1 )seminorm and penalty terms. The second part of the thesis deals with the realization of fluidstructure interaction problem of the compressible viscous flow with the elastic structure. The timedependence of the domain occupied by the fluid is treated by the ALE (Arbitrary LagrangianEulerian) method, when the compress ible NavierStokes equations are formulated in...
