Number of found documents: 367
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On the boundary conditions in the numerical simulation of stably stratified fluids flows
Bodnár, Tomáš; Fraunié, P.
2017 - English
This paper presents the results of a numerical study of the stably stratified flow over a low smooth hill. The emphasize is on certain problems related to artificial boundary conditions used in the numerical simulations. The numerical results of three-dimensional simulations are shown for a range of Froude and Reynolds numbers in order to demonstrate the varying importance of these boundary issues in different flow regimes. The simulations were performed using the Boussinesq approximation model solved by a high-resolution numerical code. The in-house developed code is based on compact finite-difference discretization in space and Strong Stability Preserving Runge–Kutta time integration. Keywords: Boussinesq approximation; stable stratification; compact finite-difference Available on request at various institutes of the ASCR
On the boundary conditions in the numerical simulation of stably stratified fluids flows

This paper presents the results of a numerical study of the stably stratified flow over a low smooth hill. The emphasize is on certain problems related to artificial boundary conditions used in the ...

Bodnár, Tomáš; Fraunié, P.
Matematický ústav, 2017

The role of Sommerville tetrahedra in numerical mathematics
Hošek, Radim
2017 - English
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by its direct generalization to any dimension. Keywords: simplicial tessellations; simplicial mesh; Sommerville tetrahedron Available in digital repository of the ASCR
The role of Sommerville tetrahedra in numerical mathematics

In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine ...

Hošek, Radim
Matematický ústav, 2017

A particular smooth interpolation that generates splines
Segeth, Karel
2017 - English
There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $it smooth interpolation$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline. Keywords: data interpolation; smooth interpolation; spline interpolation Available in digital repository of the ASCR
A particular smooth interpolation that generates splines

There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one ...

Segeth, Karel
Matematický ústav, 2017

Note on the problem of dissipative measure-valued solutions to the compressible non-Newtonian system
Al Baba, Hind; Caggio, Matteo; Ducomet, B.; Nečasová, Šárka
2017 - English
We introduce a dissipative measure-valued solution to the compressible non-Newtonian system. We generalized a result given by Novotný, Nečasová [14]. We derive a relative entropy inequality for measure-valued solution as an extension of the "classical" entropy inequality introduced by Dafermos [2], Mellet-Vasseur [11], Feireisl-Jin-Novotný [5]. Keywords: dissipative measure-valued solution; non-Newtonian fluid; compressible fluid Available on request at various institutes of the ASCR
Note on the problem of dissipative measure-valued solutions to the compressible non-Newtonian system

We introduce a dissipative measure-valued solution to the compressible non-Newtonian system. We generalized a result given by Novotný, Nečasová [14]. We derive a relative entropy inequality for ...

Al Baba, Hind; Caggio, Matteo; Ducomet, B.; Nečasová, Šárka
Matematický ústav, 2017

Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence
Caggio, Matteo; Bodnár, Tomáš
2017 - English
The aim of this short communication is to briefly introduce the Camassa-Holm equations as a working model for simulation of incompressible fluid turbulence. In particular we discuss its application for turbulent boundary layer flows. This model (and related models) is studied for several years in mathematical community, starting from Leray [23]. It can be understood as a generalization of some classical fluid models (Navier-Stokes equations, Prandtl boundary layer equations), showing some interesting mathematical properties in the analysis of the behavior of it's solution (e.g. Layton and Lewandowski [22]). It has been found however, that the model predictions can lead to surprising extensions of the use of the model in technical applications, namely in simulating the turbulent fluid flows. This brief paper should be understood as an introductory note to this novel class of models for applied scientists. Keywords: Camassa-Holm equations; turbulent boundary layer Available on request at various institutes of the ASCR
Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence

The aim of this short communication is to briefly introduce the Camassa-Holm equations as a working model for simulation of incompressible fluid turbulence. In particular we discuss its application ...

Caggio, Matteo; Bodnár, Tomáš
Matematický ústav, 2017

Znovuobjevování geometrických konstrukcí
Roubíček, Filip
2016 - Czech
Článek je věnován uplatnění principů badatelsky orientovaného vyučování matematice v didaktickém semináři určeném studentům učitelství prvního stupně základní školy, konkrétně aktivitě zaměřené na konstruování známých geometrických útvarů v prostředí překládaného papíru. V článku je popsáno sedm studentských postupů konstrukce čtverce. The paper deals with the application of principles of inquiry based mathematics education in seminars of didactics for future primary school teachers, specifically with the activity focused on construction of known geometrical figures in the environment of folding paper. Seven students´ construction procedures of a square are presented in the paper. Keywords: mathematics education; inquiry; elementary geometry Available at various institutes of the ASCR
Znovuobjevování geometrických konstrukcí

Článek je věnován uplatnění principů badatelsky orientovaného vyučování matematice v didaktickém semináři určeném studentům učitelství prvního stupně základní školy, konkrétně aktivitě zaměřené na ...

Roubíček, Filip
Matematický ústav, 2016

Word problems of a given structure in the perspective of teacher training
Tichá, Marie; Hošpesová, A.
2016 - English
The paper reports on the results of a research study focusing on how to train prospective teachers for guiding their pupils through the process of solving word problems. The teaching experiment involved prospective teachers’ work with graphical representations called branched chains to solve and pose word problems. The paper shows the difficulties the students were facing, presents ideas from discussions during joint reflection, tries to describe the changes in the students’ skills and attitudes. It also points at the differences between prospective primary and secondary mathematics teachers. Keywords: inquiry based mathematics education; prospective teaching training; subject matter knowledge; knowledge base for teaching Fulltext is available at external website.
Word problems of a given structure in the perspective of teacher training

The paper reports on the results of a research study focusing on how to train prospective teachers for guiding their pupils through the process of solving word problems. The teaching experiment ...

Tichá, Marie; Hošpesová, A.
Matematický ústav, 2016

Cosmology on Small Scales 2016: Local Hubble Expansion and Selected Controversies in Cosmology
Křížek, Michal; Dumin, Y. V.
2016 - English
The problem of cosmological expansion on small scales (e.g., inside planetary systems) has a long history, dating back to the papers (McVittie, 1932, 1933), and quite many researchers dealt with this topic in the subsequent few decades. Although most of them concluded that the Hubble expansion should be strongly suppressed at small distances, there is no commonly-established criterion for such suppression at present. Moreover, some of the widely-used theoretical arguments against the local Hubble expansion contradict each other. Keywords: cosmology Fulltext is available at external website.
Cosmology on Small Scales 2016: Local Hubble Expansion and Selected Controversies in Cosmology

The problem of cosmological expansion on small scales (e.g., inside planetary systems) has a long history, dating back to the papers (McVittie, 1932, 1933), and quite many researchers dealt with this ...

Křížek, Michal; Dumin, Y. V.
Matematický ústav, 2016

Badatelsky orientované vzdělávání jako jedna z cest ke zkvalitňování profesionality učitelů
Tichá, Marie; Samková, L.
2016 - Czech
Příspěvek je zaměřen na badatelsky orientované vzdělávání jako možnou cestu rozvíjení a zkvalitňování profesionality v přípravě učitelů 1. stupně základní školy. Vzhledem k tomu, že proces bádání vede k domněnkám, hypotetickým odpovědím a ty je třeba ověřit, zaměřili jsme se v poslední době také na rozvíjení uvědomování si potřeby argumentovat, vědomě zařazovat odůvodňování do vyučování matematice. This contribution focuses on inquiry-based education as one of the ways to develop and improve professionalism of future primary school teachers. Since the process of inquiry leads to conjectures and hypotheses that need to be verified, we recently turned our attention also to developing awareness of the need of proper argumentation and its incorporation into mathematics lessons. Keywords: inquiry-based education; teachers professionalism; primary school; argumentation Available at various institutes of the ASCR
Badatelsky orientované vzdělávání jako jedna z cest ke zkvalitňování profesionality učitelů

Příspěvek je zaměřen na badatelsky orientované vzdělávání jako možnou cestu rozvíjení a zkvalitňování profesionality v přípravě učitelů 1. stupně základní školy. Vzhledem k tomu, že proces bádání vede ...

Tichá, Marie; Samková, L.
Matematický ústav, 2016

On the Friedmann equation for the three-dimensional hypersphere
Křížek, Michal; Mészáros, A.
2016 - English
The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an expanding threedimensional sphere which enabled him to avoid boundary conditions. However, his description was very brief. Therefore, the main objective of this article is to detailed a derivation of the Friedmann equation for an unknown expansion function a = a(t) representing the radius of the universe. Furthermore, we present serious arguments showing why the validity of Einstein’s equations should not be extrapolated to the entire universe. Keywords: Einstein's equations; standard cosmological model; dark matter; dark energy Available in digital repository of the ASCR
On the Friedmann equation for the three-dimensional hypersphere

The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an ...

Křížek, Michal; Mészáros, A.
Matematický ústav, 2016

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